Add spectrum analyzer demo app

This application is a demo which uses the QtMultimedia APIs to
capture and play back PCM audio.  While either recording or playback
is ongoing, the application performs real-time level and frequency
spectrum analysis.

Reviewed-by: Alessandro Portale

55 files changed, 8296 insertions, 0 deletions

diff --git a/demos/spectrum/fftreal/Array.h b/demos/spectrum/fftreal/Array.h
new file mode 100644
index 0000000..a08e3cf
--- /dev/null
+++ b/demos/spectrum/fftreal/Array.h
@@ -0,0 +1,97 @@
+/*****************************************************************************
+
+        Array.h
+        Copyright (c) 2005 Laurent de Soras
+
+--- Legal stuff ---
+
+This library is free software; you can redistribute it and/or
+modify it under the terms of the GNU Lesser General Public
+License as published by the Free Software Foundation; either
+version 2.1 of the License, or (at your option) any later version.
+
+This library is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+Lesser General Public License for more details.
+
+You should have received a copy of the GNU Lesser General Public
+License along with this library; if not, write to the Free Software
+Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
+
+*Tab=3***********************************************************************/
+
+
+
+#if ! defined (Array_HEADER_INCLUDED)
+#define	Array_HEADER_INCLUDED
+
+#if defined (_MSC_VER)
+	#pragma once
+	#pragma warning (4 : 4250) // "Inherits via dominance."
+#endif
+
+
+
+/*\\\ INCLUDE FILES \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+
+
+template <class T, long LEN>
+class Array
+{
+
+/*\\\ PUBLIC \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+public:
+
+	typedef	T	DataType;
+
+						Array ();
+
+	inline const DataType &
+						operator [] (long pos) const;
+	inline DataType &
+						operator [] (long pos);
+
+	static inline long
+						size ();
+
+
+
+/*\\\ PROTECTED \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+protected:
+
+
+
+/*\\\ PRIVATE \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+private:
+
+	DataType			_data_arr [LEN];
+
+
+
+/*\\\ FORBIDDEN MEMBER FUNCTIONS \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+private:
+
+						Array (const Array &other);
+	Array &			operator = (const Array &other);
+	bool				operator == (const Array &other);
+	bool				operator != (const Array &other);
+
+};	// class Array
+
+
+
+#include	"Array.hpp"
+
+
+
+#endif	// Array_HEADER_INCLUDED
+
+
+
+/*\\\ EOF \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
diff --git a/demos/spectrum/fftreal/Array.hpp b/demos/spectrum/fftreal/Array.hpp
new file mode 100644
index 0000000..8300077
--- /dev/null
+++ b/demos/spectrum/fftreal/Array.hpp
@@ -0,0 +1,98 @@
+/*****************************************************************************
+
+        Array.hpp
+        Copyright (c) 2005 Laurent de Soras
+
+--- Legal stuff ---
+
+This library is free software; you can redistribute it and/or
+modify it under the terms of the GNU Lesser General Public
+License as published by the Free Software Foundation; either
+version 2.1 of the License, or (at your option) any later version.
+
+This library is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+Lesser General Public License for more details.
+
+You should have received a copy of the GNU Lesser General Public
+License along with this library; if not, write to the Free Software
+Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
+
+*Tab=3***********************************************************************/
+
+
+
+#if defined (Array_CURRENT_CODEHEADER)
+	#error Recursive inclusion of Array code header.
+#endif
+#define	Array_CURRENT_CODEHEADER
+
+#if ! defined (Array_CODEHEADER_INCLUDED)
+#define	Array_CODEHEADER_INCLUDED
+
+
+
+/*\\\ INCLUDE FILES \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+#include	<cassert>
+
+
+
+/*\\\ PUBLIC \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+
+
+template <class T, long LEN>
+Array <T, LEN>::Array ()
+{
+	// Nothing
+}
+
+
+
+template <class T, long LEN>
+const typename Array <T, LEN>::DataType &	Array <T, LEN>::operator [] (long pos) const
+{
+	assert (pos >= 0);
+	assert (pos < LEN);
+
+	return (_data_arr [pos]);
+}
+
+
+
+template <class T, long LEN>
+typename Array <T, LEN>::DataType &	Array <T, LEN>::operator [] (long pos)
+{
+	assert (pos >= 0);
+	assert (pos < LEN);
+
+	return (_data_arr [pos]);
+}
+
+
+
+template <class T, long LEN>
+long	Array <T, LEN>::size ()
+{
+	return (LEN);
+}
+
+
+
+/*\\\ PROTECTED \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+
+
+/*\\\ PRIVATE \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+
+
+#endif	// Array_CODEHEADER_INCLUDED
+
+#undef Array_CURRENT_CODEHEADER
+
+
+
+/*\\\ EOF \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
diff --git a/demos/spectrum/fftreal/DynArray.h b/demos/spectrum/fftreal/DynArray.h
new file mode 100644
index 0000000..8041a0c
--- /dev/null
+++ b/demos/spectrum/fftreal/DynArray.h
@@ -0,0 +1,100 @@
+/*****************************************************************************
+
+        DynArray.h
+        Copyright (c) 2005 Laurent de Soras
+
+--- Legal stuff ---
+
+This library is free software; you can redistribute it and/or
+modify it under the terms of the GNU Lesser General Public
+License as published by the Free Software Foundation; either
+version 2.1 of the License, or (at your option) any later version.
+
+This library is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+Lesser General Public License for more details.
+
+You should have received a copy of the GNU Lesser General Public
+License along with this library; if not, write to the Free Software
+Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
+
+*Tab=3***********************************************************************/
+
+
+
+#if ! defined (DynArray_HEADER_INCLUDED)
+#define	DynArray_HEADER_INCLUDED
+
+#if defined (_MSC_VER)
+	#pragma once
+	#pragma warning (4 : 4250) // "Inherits via dominance."
+#endif
+
+
+
+/*\\\ INCLUDE FILES \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+
+
+template <class T>
+class DynArray
+{
+
+/*\\\ PUBLIC \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+public:
+
+	typedef	T	DataType;
+
+						DynArray ();
+	explicit			DynArray (long size);
+						~DynArray ();
+
+	inline long		size () const;
+	inline void		resize (long size);
+
+	inline const DataType &
+						operator [] (long pos) const;
+	inline DataType &
+						operator [] (long pos);
+
+
+
+/*\\\ PROTECTED \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+protected:
+
+
+
+/*\\\ PRIVATE \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+private:
+
+	DataType *		_data_ptr;
+	long				_len;
+
+
+
+/*\\\ FORBIDDEN MEMBER FUNCTIONS \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+private:
+
+						DynArray (const DynArray &other);
+	DynArray &		operator = (const DynArray &other);
+	bool				operator == (const DynArray &other);
+	bool				operator != (const DynArray &other);
+
+};	// class DynArray
+
+
+
+#include	"DynArray.hpp"
+
+
+
+#endif	// DynArray_HEADER_INCLUDED
+
+
+
+/*\\\ EOF \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
diff --git a/demos/spectrum/fftreal/DynArray.hpp b/demos/spectrum/fftreal/DynArray.hpp
new file mode 100644
index 0000000..e62b10f
--- /dev/null
+++ b/demos/spectrum/fftreal/DynArray.hpp
@@ -0,0 +1,143 @@
+/*****************************************************************************
+
+        DynArray.hpp
+        Copyright (c) 2005 Laurent de Soras
+
+--- Legal stuff ---
+
+This library is free software; you can redistribute it and/or
+modify it under the terms of the GNU Lesser General Public
+License as published by the Free Software Foundation; either
+version 2.1 of the License, or (at your option) any later version.
+
+This library is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+Lesser General Public License for more details.
+
+You should have received a copy of the GNU Lesser General Public
+License along with this library; if not, write to the Free Software
+Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
+
+*Tab=3***********************************************************************/
+
+
+
+#if defined (DynArray_CURRENT_CODEHEADER)
+	#error Recursive inclusion of DynArray code header.
+#endif
+#define	DynArray_CURRENT_CODEHEADER
+
+#if ! defined (DynArray_CODEHEADER_INCLUDED)
+#define	DynArray_CODEHEADER_INCLUDED
+
+
+
+/*\\\ INCLUDE FILES \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+#include	<cassert>
+
+
+
+/*\\\ PUBLIC \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+
+
+template <class T>
+DynArray <T>::DynArray ()
+:	_data_ptr (0)
+,	_len (0)
+{
+	// Nothing
+}
+
+
+
+template <class T>
+DynArray <T>::DynArray (long size)
+:	_data_ptr (0)
+,	_len (0)
+{
+	assert (size >= 0);
+	if (size > 0)
+	{
+		_data_ptr = new DataType [size];
+		_len = size;
+	}
+}
+
+
+
+template <class T>
+DynArray <T>::~DynArray ()
+{
+	delete [] _data_ptr;
+	_data_ptr = 0;
+	_len = 0;
+}
+
+
+
+template <class T>
+long	DynArray <T>::size () const
+{
+	return (_len);
+}
+
+
+
+template <class T>
+void	DynArray <T>::resize (long size)
+{
+	assert (size >= 0);
+	if (size > 0)
+	{
+		DataType *		old_data_ptr = _data_ptr;
+		DataType *		tmp_data_ptr = new DataType [size];
+
+		_data_ptr = tmp_data_ptr;
+		_len = size;
+
+		delete [] old_data_ptr;
+	}
+}
+
+
+
+template <class T>
+const typename DynArray <T>::DataType &	DynArray <T>::operator [] (long pos) const
+{
+	assert (pos >= 0);
+	assert (pos < _len);
+
+	return (_data_ptr [pos]);
+}
+
+
+
+template <class T>
+typename DynArray <T>::DataType &	DynArray <T>::operator [] (long pos)
+{
+	assert (pos >= 0);
+	assert (pos < _len);
+
+	return (_data_ptr [pos]);
+}
+
+
+
+/*\\\ PROTECTED \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+
+
+/*\\\ PRIVATE \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+
+
+#endif	// DynArray_CODEHEADER_INCLUDED
+
+#undef DynArray_CURRENT_CODEHEADER
+
+
+
+/*\\\ EOF \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
diff --git a/demos/spectrum/fftreal/FFTReal.dsp b/demos/spectrum/fftreal/FFTReal.dsp
new file mode 100644
index 0000000..fe970db
--- /dev/null
+++ b/demos/spectrum/fftreal/FFTReal.dsp
@@ -0,0 +1,273 @@
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+# Microsoft Developer Studio Generated Build File, Format Version 6.00
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+
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+CFG=FFTReal - Win32 Debug
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+
+# PROP BASE Use_MFC 0
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+!ELSEIF  "$(CFG)" == "FFTReal - Win32 Debug"
+
+# PROP BASE Use_MFC 0
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+
+!ENDIF 
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+# Begin Target
+
+# Name "FFTReal - Win32 Release"
+# Name "FFTReal - Win32 Debug"
+# Begin Group "Library"
+
+# PROP Default_Filter ""
+# Begin Source File
+
+SOURCE=.\Array.h
+# End Source File
+# Begin Source File
+
+SOURCE=.\Array.hpp
+# End Source File
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+SOURCE=.\def.h
+# End Source File
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+# End Source File
+# Begin Source File
+
+SOURCE=.\DynArray.hpp
+# End Source File
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+# End Source File
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+# End Source File
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+# End Source File
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+# End Source File
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+# End Source File
+# Begin Source File
+
+SOURCE=.\FFTRealPassDirect.h
+# End Source File
+# Begin Source File
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+SOURCE=.\FFTRealPassDirect.hpp
+# End Source File
+# Begin Source File
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+SOURCE=.\FFTRealPassInverse.h
+# End Source File
+# Begin Source File
+
+SOURCE=.\FFTRealPassInverse.hpp
+# End Source File
+# Begin Source File
+
+SOURCE=.\FFTRealSelect.h
+# End Source File
+# Begin Source File
+
+SOURCE=.\FFTRealSelect.hpp
+# End Source File
+# Begin Source File
+
+SOURCE=.\FFTRealUseTrigo.h
+# End Source File
+# Begin Source File
+
+SOURCE=.\FFTRealUseTrigo.hpp
+# End Source File
+# Begin Source File
+
+SOURCE=.\OscSinCos.h
+# End Source File
+# Begin Source File
+
+SOURCE=.\OscSinCos.hpp
+# End Source File
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+# End Source File
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diff --git a/demos/spectrum/fftreal/FFTReal.dsw b/demos/spectrum/fftreal/FFTReal.dsw
new file mode 100644
index 0000000..076b0ae
--- /dev/null
+++ b/demos/spectrum/fftreal/FFTReal.dsw
@@ -0,0 +1,29 @@
+Microsoft Developer Studio Workspace File, Format Version 6.00
+# WARNING: DO NOT EDIT OR DELETE THIS WORKSPACE FILE!
+
+###############################################################################
+
+Project: "FFTReal"=.\FFTReal.dsp - Package Owner=<4>
+
+Package=<5>
+{{{
+}}}
+
+Package=<4>
+{{{
+}}}
+
+###############################################################################
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+
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diff --git a/demos/spectrum/fftreal/FFTReal.h b/demos/spectrum/fftreal/FFTReal.h
new file mode 100644
index 0000000..9fb2725
--- /dev/null
+++ b/demos/spectrum/fftreal/FFTReal.h
@@ -0,0 +1,142 @@
+/*****************************************************************************
+
+        FFTReal.h
+        Copyright (c) 2005 Laurent de Soras
+
+--- Legal stuff ---
+
+This library is free software; you can redistribute it and/or
+modify it under the terms of the GNU Lesser General Public
+License as published by the Free Software Foundation; either
+version 2.1 of the License, or (at your option) any later version.
+
+This library is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+Lesser General Public License for more details.
+
+You should have received a copy of the GNU Lesser General Public
+License along with this library; if not, write to the Free Software
+Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
+
+*Tab=3***********************************************************************/
+
+
+
+#if ! defined (FFTReal_HEADER_INCLUDED)
+#define	FFTReal_HEADER_INCLUDED
+
+#if defined (_MSC_VER)
+	#pragma once
+	#pragma warning (4 : 4250) // "Inherits via dominance."
+#endif
+
+
+
+/*\\\ INCLUDE FILES \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+#include	"def.h"
+#include	"DynArray.h"
+#include	"OscSinCos.h"
+
+
+
+template <class DT>
+class FFTReal
+{
+
+/*\\\ PUBLIC \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+public:
+
+	enum {			MAX_BIT_DEPTH	= 30	};	// So length can be represented as long int
+
+	typedef	DT	DataType;
+
+	explicit			FFTReal (long length);
+	virtual			~FFTReal () {}
+
+	long				get_length () const;
+	void				do_fft (DataType f [], const DataType x []) const;
+	void				do_ifft (const DataType f [], DataType x []) const;
+	void				rescale (DataType x []) const;
+	DataType *		use_buffer () const;
+
+
+
+/*\\\ PROTECTED \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+protected:
+
+
+
+/*\\\ PRIVATE \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+private:
+
+   // Over this bit depth, we use direct calculation for sin/cos
+   enum {	      TRIGO_BD_LIMIT	= 12  };
+
+	typedef	OscSinCos <DataType>	OscType;
+
+	void				init_br_lut ();
+	void				init_trigo_lut ();
+	void				init_trigo_osc ();
+
+	FORCEINLINE const long *
+						get_br_ptr () const;
+	FORCEINLINE const DataType	*
+						get_trigo_ptr (int level) const;
+	FORCEINLINE long
+						get_trigo_level_index (int level) const;
+
+	inline void		compute_fft_general (DataType f [], const DataType x []) const;
+	inline void		compute_direct_pass_1_2 (DataType df [], const DataType x []) const;
+	inline void		compute_direct_pass_3 (DataType df [], const DataType sf []) const;
+	inline void		compute_direct_pass_n (DataType df [], const DataType sf [], int pass) const;
+	inline void		compute_direct_pass_n_lut (DataType df [], const DataType sf [], int pass) const;
+	inline void		compute_direct_pass_n_osc (DataType df [], const DataType sf [], int pass) const;
+
+	inline void		compute_ifft_general (const DataType f [], DataType x []) const;
+	inline void		compute_inverse_pass_n (DataType df [], const DataType sf [], int pass) const;
+	inline void		compute_inverse_pass_n_osc (DataType df [], const DataType sf [], int pass) const;
+	inline void		compute_inverse_pass_n_lut (DataType df [], const DataType sf [], int pass) const;
+	inline void		compute_inverse_pass_3 (DataType df [], const DataType sf []) const;
+	inline void		compute_inverse_pass_1_2 (DataType x [], const DataType sf []) const;
+
+	const long		_length;
+	const int		_nbr_bits;
+	DynArray <long>
+						_br_lut;
+	DynArray <DataType>
+						_trigo_lut;
+	mutable DynArray <DataType>
+						_buffer;
+   mutable DynArray <OscType>
+						_trigo_osc;
+
+
+
+/*\\\ FORBIDDEN MEMBER FUNCTIONS \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+private:
+
+						FFTReal ();
+						FFTReal (const FFTReal &other);
+	FFTReal &		operator = (const FFTReal &other);
+	bool				operator == (const FFTReal &other);
+	bool				operator != (const FFTReal &other);
+
+};	// class FFTReal
+
+
+
+#include	"FFTReal.hpp"
+
+
+
+#endif	// FFTReal_HEADER_INCLUDED
+
+
+
+/*\\\ EOF \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
diff --git a/demos/spectrum/fftreal/FFTReal.hpp b/demos/spectrum/fftreal/FFTReal.hpp
new file mode 100644
index 0000000..335d771
--- /dev/null
+++ b/demos/spectrum/fftreal/FFTReal.hpp
@@ -0,0 +1,916 @@
+/*****************************************************************************
+
+        FFTReal.hpp
+        Copyright (c) 2005 Laurent de Soras
+
+--- Legal stuff ---
+
+This library is free software; you can redistribute it and/or
+modify it under the terms of the GNU Lesser General Public
+License as published by the Free Software Foundation; either
+version 2.1 of the License, or (at your option) any later version.
+
+This library is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+Lesser General Public License for more details.
+
+You should have received a copy of the GNU Lesser General Public
+License along with this library; if not, write to the Free Software
+Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
+
+*Tab=3***********************************************************************/
+
+
+
+#if defined (FFTReal_CURRENT_CODEHEADER)
+	#error Recursive inclusion of FFTReal code header.
+#endif
+#define	FFTReal_CURRENT_CODEHEADER
+
+#if ! defined (FFTReal_CODEHEADER_INCLUDED)
+#define	FFTReal_CODEHEADER_INCLUDED
+
+
+
+/*\\\ INCLUDE FILES \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+#include	<cassert>
+#include	<cmath>
+
+
+
+static inline bool	FFTReal_is_pow2 (long x)
+{
+	assert (x > 0);
+
+	return  ((x & -x) == x);
+}
+
+
+
+static inline int	FFTReal_get_next_pow2 (long x)
+{
+	--x;
+
+	int				p = 0;
+	while ((x & ~0xFFFFL) != 0)
+	{
+		p += 16;
+		x >>= 16;
+	}
+	while ((x & ~0xFL) != 0)
+	{
+		p += 4;
+		x >>= 4;
+	}
+	while (x > 0)
+	{
+		++p;
+		x >>= 1;
+	}
+
+	return (p);
+}
+
+
+
+/*\\\ PUBLIC \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+
+
+/*
+==============================================================================
+Name: ctor
+Input parameters:
+	- length: length of the array on which we want to do a FFT. Range: power of
+		2 only, > 0.
+Throws: std::bad_alloc
+==============================================================================
+*/
+
+template <class DT>
+FFTReal <DT>::FFTReal (long length)
+:	_length (length)
+,	_nbr_bits (FFTReal_get_next_pow2 (length))
+,	_br_lut ()
+,	_trigo_lut ()
+,	_buffer (length)
+,	_trigo_osc ()
+{
+	assert (FFTReal_is_pow2 (length));
+	assert (_nbr_bits <= MAX_BIT_DEPTH);
+
+	init_br_lut ();
+	init_trigo_lut ();
+	init_trigo_osc ();
+}
+
+
+
+/*
+==============================================================================
+Name: get_length
+Description:
+	Returns the number of points processed by this FFT object.
+Returns: The number of points, power of 2, > 0.
+Throws: Nothing
+==============================================================================
+*/
+
+template <class DT>
+long	FFTReal <DT>::get_length () const
+{
+	return (_length);
+}
+
+
+
+/*
+==============================================================================
+Name: do_fft
+Description:
+	Compute the FFT of the array.
+Input parameters:
+	- x: pointer on the source array (time).
+Output parameters:
+	- f: pointer on the destination array (frequencies).
+		f [0...length(x)/2] = real values,
+		f [length(x)/2+1...length(x)-1] = negative imaginary values of
+		coefficents 1...length(x)/2-1.
+Throws: Nothing
+==============================================================================
+*/
+
+template <class DT>
+void	FFTReal <DT>::do_fft (DataType f [], const DataType x []) const
+{
+	assert (f != 0);
+	assert (f != use_buffer ());
+	assert (x != 0);
+	assert (x != use_buffer ());
+	assert (x != f);
+
+	// General case
+	if (_nbr_bits > 2)
+	{
+		compute_fft_general (f, x);
+	}
+
+	// 4-point FFT
+	else if (_nbr_bits == 2)
+	{
+		f [1] = x [0] - x [2];
+		f [3] = x [1] - x [3];
+
+		const DataType	b_0 = x [0] + x [2];
+		const DataType	b_2 = x [1] + x [3];
+		
+		f [0] = b_0 + b_2;
+		f [2] = b_0 - b_2;
+	}
+
+	// 2-point FFT
+	else if (_nbr_bits == 1)
+	{
+		f [0] = x [0] + x [1];
+		f [1] = x [0] - x [1];
+	}
+
+	// 1-point FFT
+	else
+	{
+		f [0] = x [0];
+	}
+}
+
+
+
+/*
+==============================================================================
+Name: do_ifft
+Description:
+	Compute the inverse FFT of the array. Note that data must be post-scaled:
+	IFFT (FFT (x)) = x * length (x).
+Input parameters:
+	- f: pointer on the source array (frequencies).
+		f [0...length(x)/2] = real values
+		f [length(x)/2+1...length(x)-1] = negative imaginary values of
+		coefficents 1...length(x)/2-1.
+Output parameters:
+	- x: pointer on the destination array (time).
+Throws: Nothing
+==============================================================================
+*/
+
+template <class DT>
+void	FFTReal <DT>::do_ifft (const DataType f [], DataType x []) const
+{
+	assert (f != 0);
+	assert (f != use_buffer ());
+	assert (x != 0);
+	assert (x != use_buffer ());
+	assert (x != f);
+
+	// General case
+	if (_nbr_bits > 2)
+	{
+		compute_ifft_general (f, x);
+	}
+
+	// 4-point IFFT
+	else if (_nbr_bits == 2)
+	{
+		const DataType	b_0 = f [0] + f [2];
+		const DataType	b_2 = f [0] - f [2];
+
+		x [0] = b_0 + f [1] * 2;
+		x [2] = b_0 - f [1] * 2;
+		x [1] = b_2 + f [3] * 2;
+		x [3] = b_2 - f [3] * 2;
+	}
+
+	// 2-point IFFT
+	else if (_nbr_bits == 1)
+	{
+		x [0] = f [0] + f [1];
+		x [1] = f [0] - f [1];
+	}
+
+	// 1-point IFFT
+	else
+	{
+		x [0] = f [0];
+	}
+}
+
+
+
+/*
+==============================================================================
+Name: rescale
+Description:
+	Scale an array by divide each element by its length. This function should
+	be called after FFT + IFFT.
+Input parameters:
+	- x: pointer on array to rescale (time or frequency).
+Throws: Nothing
+==============================================================================
+*/
+
+template <class DT>
+void	FFTReal <DT>::rescale (DataType x []) const
+{
+	const DataType	mul = DataType (1.0 / _length);
+
+	if (_length < 4)
+	{
+		long				i = _length - 1;
+		do
+		{
+			x [i] *= mul;
+			--i;
+		}
+		while (i >= 0);
+	}
+
+	else
+	{
+		assert ((_length & 3) == 0);
+
+		// Could be optimized with SIMD instruction sets (needs alignment check)
+		long				i = _length - 4;
+		do
+		{
+			x [i + 0] *= mul;
+			x [i + 1] *= mul;
+			x [i + 2] *= mul;
+			x [i + 3] *= mul;
+			i -= 4;
+		}
+		while (i >= 0);
+	}
+}
+
+
+
+/*
+==============================================================================
+Name: use_buffer
+Description:
+	Access the internal buffer, whose length is the FFT one.
+	Buffer content will be erased at each do_fft() / do_ifft() call!
+	This buffer cannot be used as:
+		- source for FFT or IFFT done with this object
+		- destination for FFT or IFFT done with this object
+Returns:
+	Buffer start address
+Throws: Nothing
+==============================================================================
+*/
+
+template <class DT>
+typename FFTReal <DT>::DataType *	FFTReal <DT>::use_buffer () const
+{
+	return (&_buffer [0]);
+}
+
+
+
+/*\\\ PROTECTED \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+
+
+/*\\\ PRIVATE \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+
+
+template <class DT>
+void	FFTReal <DT>::init_br_lut ()
+{
+	const long		length = 1L << _nbr_bits;
+	_br_lut.resize (length);
+
+	_br_lut [0] = 0;
+	long				br_index = 0;
+	for (long cnt = 1; cnt < length; ++cnt)
+	{
+		// ++br_index (bit reversed)
+		long				bit = length >> 1;
+		while (((br_index ^= bit) & bit) == 0)
+		{
+			bit >>= 1;
+		}
+
+		_br_lut [cnt] = br_index;
+	}
+}
+
+
+
+template <class DT>
+void	FFTReal <DT>::init_trigo_lut ()
+{
+	using namespace std;
+
+	if (_nbr_bits > 3)
+	{
+		const long		total_len = (1L << (_nbr_bits - 1)) - 4;
+		_trigo_lut.resize (total_len);
+
+		for (int level = 3; level < _nbr_bits; ++level)
+		{
+			const long		level_len = 1L << (level - 1);
+			DataType	* const	level_ptr =
+				&_trigo_lut [get_trigo_level_index (level)];
+			const double	mul = PI / (level_len << 1);
+
+			for (long i = 0; i < level_len; ++ i)
+			{
+				level_ptr [i] = static_cast <DataType> (cos (i * mul));
+			}
+		}
+	}
+}
+
+
+
+template <class DT>
+void	FFTReal <DT>::init_trigo_osc ()
+{
+	const int		nbr_osc = _nbr_bits - TRIGO_BD_LIMIT;
+	if (nbr_osc > 0)
+	{
+		_trigo_osc.resize (nbr_osc);
+
+		for (int osc_cnt = 0; osc_cnt < nbr_osc; ++osc_cnt)
+		{
+			OscType &		osc = _trigo_osc [osc_cnt];
+
+			const long		len = 1L << (TRIGO_BD_LIMIT + osc_cnt);
+			const double	mul = (0.5 * PI) / len;
+			osc.set_step (mul);
+		}
+	}
+}
+
+
+
+template <class DT>
+const long *	FFTReal <DT>::get_br_ptr () const
+{
+	return (&_br_lut [0]);
+}
+
+
+
+template <class DT>
+const typename FFTReal <DT>::DataType *	FFTReal <DT>::get_trigo_ptr (int level) const
+{
+	assert (level >= 3);
+
+	return (&_trigo_lut [get_trigo_level_index (level)]);
+}
+
+
+
+template <class DT>
+long	FFTReal <DT>::get_trigo_level_index (int level) const
+{
+	assert (level >= 3);
+
+	return ((1L << (level - 1)) - 4);
+}
+
+
+
+// Transform in several passes
+template <class DT>
+void	FFTReal <DT>::compute_fft_general (DataType f [], const DataType x []) const
+{
+	assert (f != 0);
+	assert (f != use_buffer ());
+	assert (x != 0);
+	assert (x != use_buffer ());
+	assert (x != f);
+
+	DataType *		sf;
+	DataType *		df;
+
+	if ((_nbr_bits & 1) != 0)
+	{
+		df = use_buffer ();
+		sf = f;
+	}
+	else
+	{
+		df = f;
+		sf = use_buffer ();
+	}
+
+	compute_direct_pass_1_2 (df, x);
+	compute_direct_pass_3 (sf, df);
+
+	for (int pass = 3; pass < _nbr_bits; ++ pass)
+	{
+		compute_direct_pass_n (df, sf, pass);
+
+		DataType * const	temp_ptr = df;
+		df = sf;
+		sf = temp_ptr;
+	}
+}
+
+
+
+template <class DT>
+void	FFTReal <DT>::compute_direct_pass_1_2 (DataType df [], const DataType x []) const
+{
+	assert (df != 0);
+	assert (x != 0);
+	assert (df != x);
+
+	const long * const	bit_rev_lut_ptr = get_br_ptr ();
+	long				coef_index = 0;
+	do
+	{
+		const long		rev_index_0 = bit_rev_lut_ptr [coef_index];
+		const long		rev_index_1 = bit_rev_lut_ptr [coef_index + 1];
+		const long		rev_index_2 = bit_rev_lut_ptr [coef_index + 2];
+		const long		rev_index_3 = bit_rev_lut_ptr [coef_index + 3];
+
+		DataType	* const	df2 = df + coef_index;
+		df2 [1] = x [rev_index_0] - x [rev_index_1];
+		df2 [3] = x [rev_index_2] - x [rev_index_3];
+
+		const DataType	sf_0 = x [rev_index_0] + x [rev_index_1];
+		const DataType	sf_2 = x [rev_index_2] + x [rev_index_3];
+
+		df2 [0] = sf_0 + sf_2;
+		df2 [2] = sf_0 - sf_2;
+		
+		coef_index += 4;
+	}
+	while (coef_index < _length);
+}
+
+
+
+template <class DT>
+void	FFTReal <DT>::compute_direct_pass_3 (DataType df [], const DataType sf []) const
+{
+	assert (df != 0);
+	assert (sf != 0);
+	assert (df != sf);
+
+	const DataType	sqrt2_2 = DataType (SQRT2 * 0.5);
+	long				coef_index = 0;
+	do
+	{
+		DataType			v;
+
+		df [coef_index] = sf [coef_index] + sf [coef_index + 4];
+		df [coef_index + 4] = sf [coef_index] - sf [coef_index + 4];
+		df [coef_index + 2] = sf [coef_index + 2];
+		df [coef_index + 6] = sf [coef_index + 6];
+
+		v = (sf [coef_index + 5] - sf [coef_index + 7]) * sqrt2_2;
+		df [coef_index + 1] = sf [coef_index + 1] + v;
+		df [coef_index + 3] = sf [coef_index + 1] - v;
+
+		v = (sf [coef_index + 5] + sf [coef_index + 7]) * sqrt2_2;
+		df [coef_index + 5] = v + sf [coef_index + 3];
+		df [coef_index + 7] = v - sf [coef_index + 3];
+
+		coef_index += 8;
+	}
+	while (coef_index < _length);
+}
+
+
+
+template <class DT>
+void	FFTReal <DT>::compute_direct_pass_n (DataType df [], const DataType sf [], int pass) const
+{
+	assert (df != 0);
+	assert (sf != 0);
+	assert (df != sf);
+	assert (pass >= 3);
+	assert (pass < _nbr_bits);
+
+	if (pass <= TRIGO_BD_LIMIT)
+	{
+		compute_direct_pass_n_lut (df, sf, pass);
+	}
+	else
+	{
+		compute_direct_pass_n_osc (df, sf, pass);
+	}
+}
+
+
+
+template <class DT>
+void	FFTReal <DT>::compute_direct_pass_n_lut (DataType df [], const DataType sf [], int pass) const
+{
+	assert (df != 0);
+	assert (sf != 0);
+	assert (df != sf);
+	assert (pass >= 3);
+	assert (pass < _nbr_bits);
+
+	const long		nbr_coef = 1 << pass;
+	const long		h_nbr_coef = nbr_coef >> 1;
+	const long		d_nbr_coef = nbr_coef << 1;
+	long				coef_index = 0;
+	const DataType	* const	cos_ptr = get_trigo_ptr (pass);
+	do
+	{
+		const DataType	* const	sf1r = sf + coef_index;
+		const DataType	* const	sf2r = sf1r + nbr_coef;
+		DataType			* const	dfr = df + coef_index;
+		DataType			* const	dfi = dfr + nbr_coef;
+
+		// Extreme coefficients are always real
+		dfr [0] = sf1r [0] + sf2r [0];
+		dfi [0] = sf1r [0] - sf2r [0];	// dfr [nbr_coef] =
+		dfr [h_nbr_coef] = sf1r [h_nbr_coef];
+		dfi [h_nbr_coef] = sf2r [h_nbr_coef];
+
+		// Others are conjugate complex numbers
+		const DataType * const	sf1i = sf1r + h_nbr_coef;
+		const DataType * const	sf2i = sf1i + nbr_coef;
+		for (long i = 1; i < h_nbr_coef; ++ i)
+		{
+			const DataType	c = cos_ptr [i];					// cos (i*PI/nbr_coef);
+			const DataType	s = cos_ptr [h_nbr_coef - i];	// sin (i*PI/nbr_coef);
+			DataType	 		v;
+
+			v = sf2r [i] * c - sf2i [i] * s;
+			dfr [i] = sf1r [i] + v;
+			dfi [-i] = sf1r [i] - v;	// dfr [nbr_coef - i] =
+
+			v = sf2r [i] * s + sf2i [i] * c;
+			dfi [i] = v + sf1i [i];
+			dfi [nbr_coef - i] = v - sf1i [i];
+		}
+
+		coef_index += d_nbr_coef;
+	}
+	while (coef_index < _length);
+}
+
+
+
+template <class DT>
+void	FFTReal <DT>::compute_direct_pass_n_osc (DataType df [], const DataType sf [], int pass) const
+{
+	assert (df != 0);
+	assert (sf != 0);
+	assert (df != sf);
+	assert (pass > TRIGO_BD_LIMIT);
+	assert (pass < _nbr_bits);
+
+	const long		nbr_coef = 1 << pass;
+	const long		h_nbr_coef = nbr_coef >> 1;
+	const long		d_nbr_coef = nbr_coef << 1;
+	long				coef_index = 0;
+	OscType &		osc = _trigo_osc [pass - (TRIGO_BD_LIMIT + 1)];
+	do
+	{
+		const DataType	* const	sf1r = sf + coef_index;
+		const DataType	* const	sf2r = sf1r + nbr_coef;
+		DataType			* const	dfr = df + coef_index;
+		DataType			* const	dfi = dfr + nbr_coef;
+
+		osc.clear_buffers ();
+
+		// Extreme coefficients are always real
+		dfr [0] = sf1r [0] + sf2r [0];
+		dfi [0] = sf1r [0] - sf2r [0];	// dfr [nbr_coef] =
+		dfr [h_nbr_coef] = sf1r [h_nbr_coef];
+		dfi [h_nbr_coef] = sf2r [h_nbr_coef];
+
+		// Others are conjugate complex numbers
+		const DataType * const	sf1i = sf1r + h_nbr_coef;
+		const DataType * const	sf2i = sf1i + nbr_coef;
+		for (long i = 1; i < h_nbr_coef; ++ i)
+		{
+			osc.step ();
+			const DataType	c = osc.get_cos ();
+			const DataType	s = osc.get_sin ();
+			DataType	 		v;
+
+			v = sf2r [i] * c - sf2i [i] * s;
+			dfr [i] = sf1r [i] + v;
+			dfi [-i] = sf1r [i] - v;	// dfr [nbr_coef - i] =
+
+			v = sf2r [i] * s + sf2i [i] * c;
+			dfi [i] = v + sf1i [i];
+			dfi [nbr_coef - i] = v - sf1i [i];
+		}
+
+		coef_index += d_nbr_coef;
+	}
+	while (coef_index < _length);
+}
+
+
+
+// Transform in several pass
+template <class DT>
+void	FFTReal <DT>::compute_ifft_general (const DataType f [], DataType x []) const
+{
+	assert (f != 0);
+	assert (f != use_buffer ());
+	assert (x != 0);
+	assert (x != use_buffer ());
+	assert (x != f);
+
+	DataType *		sf = const_cast <DataType *> (f);
+	DataType *		df;
+	DataType *		df_temp;
+
+	if (_nbr_bits & 1)
+	{
+		df = use_buffer ();
+		df_temp = x;
+	}
+	else
+	{
+		df = x;
+		df_temp = use_buffer ();
+	}
+
+	for (int pass = _nbr_bits - 1; pass >= 3; -- pass)
+	{
+		compute_inverse_pass_n (df, sf, pass);
+
+		if (pass < _nbr_bits - 1)
+		{
+			DataType	* const	temp_ptr = df;
+			df = sf;
+			sf = temp_ptr;
+		}
+		else
+		{
+			sf = df;
+			df = df_temp;
+		}
+	}
+
+	compute_inverse_pass_3 (df, sf);
+	compute_inverse_pass_1_2 (x, df);
+}
+
+
+
+template <class DT>
+void	FFTReal <DT>::compute_inverse_pass_n (DataType df [], const DataType sf [], int pass) const
+{
+	assert (df != 0);
+	assert (sf != 0);
+	assert (df != sf);
+	assert (pass >= 3);
+	assert (pass < _nbr_bits);
+
+	if (pass <= TRIGO_BD_LIMIT)
+	{
+		compute_inverse_pass_n_lut (df, sf, pass);
+	}
+	else
+	{
+		compute_inverse_pass_n_osc (df, sf, pass);
+	}
+}
+
+
+
+template <class DT>
+void	FFTReal <DT>::compute_inverse_pass_n_lut (DataType df [], const DataType sf [], int pass) const
+{
+	assert (df != 0);
+	assert (sf != 0);
+	assert (df != sf);
+	assert (pass >= 3);
+	assert (pass < _nbr_bits);
+
+	const long		nbr_coef = 1 << pass;
+	const long		h_nbr_coef = nbr_coef >> 1;
+	const long		d_nbr_coef = nbr_coef << 1;
+	long				coef_index = 0;
+	const DataType * const	cos_ptr = get_trigo_ptr (pass);
+	do
+	{
+		const DataType	* const	sfr = sf + coef_index;
+		const DataType	* const	sfi = sfr + nbr_coef;
+		DataType			* const	df1r = df + coef_index;
+		DataType			* const	df2r = df1r + nbr_coef;
+
+		// Extreme coefficients are always real
+		df1r [0] = sfr [0] + sfi [0];		// + sfr [nbr_coef]
+		df2r [0] = sfr [0] - sfi [0];		// - sfr [nbr_coef]
+		df1r [h_nbr_coef] = sfr [h_nbr_coef] * 2;
+		df2r [h_nbr_coef] = sfi [h_nbr_coef] * 2;
+
+		// Others are conjugate complex numbers
+		DataType * const	df1i = df1r + h_nbr_coef;
+		DataType * const	df2i = df1i + nbr_coef;
+		for (long i = 1; i < h_nbr_coef; ++ i)
+		{
+			df1r [i] = sfr [i] + sfi [-i];		// + sfr [nbr_coef - i]
+			df1i [i] = sfi [i] - sfi [nbr_coef - i];
+
+			const DataType	c = cos_ptr [i];					// cos (i*PI/nbr_coef);
+			const DataType	s = cos_ptr [h_nbr_coef - i];	// sin (i*PI/nbr_coef);
+			const DataType	vr = sfr [i] - sfi [-i];		// - sfr [nbr_coef - i]
+			const DataType	vi = sfi [i] + sfi [nbr_coef - i];
+
+			df2r [i] = vr * c + vi * s;
+			df2i [i] = vi * c - vr * s;
+		}
+
+		coef_index += d_nbr_coef;
+	}
+	while (coef_index < _length);
+}
+
+
+
+template <class DT>
+void	FFTReal <DT>::compute_inverse_pass_n_osc (DataType df [], const DataType sf [], int pass) const
+{
+	assert (df != 0);
+	assert (sf != 0);
+	assert (df != sf);
+	assert (pass > TRIGO_BD_LIMIT);
+	assert (pass < _nbr_bits);
+
+	const long		nbr_coef = 1 << pass;
+	const long		h_nbr_coef = nbr_coef >> 1;
+	const long		d_nbr_coef = nbr_coef << 1;
+	long				coef_index = 0;
+	OscType &		osc = _trigo_osc [pass - (TRIGO_BD_LIMIT + 1)];
+	do
+	{
+		const DataType	* const	sfr = sf + coef_index;
+		const DataType	* const	sfi = sfr + nbr_coef;
+		DataType			* const	df1r = df + coef_index;
+		DataType			* const	df2r = df1r + nbr_coef;
+
+		osc.clear_buffers ();
+
+		// Extreme coefficients are always real
+		df1r [0] = sfr [0] + sfi [0];		// + sfr [nbr_coef]
+		df2r [0] = sfr [0] - sfi [0];		// - sfr [nbr_coef]
+		df1r [h_nbr_coef] = sfr [h_nbr_coef] * 2;
+		df2r [h_nbr_coef] = sfi [h_nbr_coef] * 2;
+
+		// Others are conjugate complex numbers
+		DataType * const	df1i = df1r + h_nbr_coef;
+		DataType * const	df2i = df1i + nbr_coef;
+		for (long i = 1; i < h_nbr_coef; ++ i)
+		{
+			df1r [i] = sfr [i] + sfi [-i];		// + sfr [nbr_coef - i]
+			df1i [i] = sfi [i] - sfi [nbr_coef - i];
+
+			osc.step ();
+			const DataType	c = osc.get_cos ();
+			const DataType	s = osc.get_sin ();
+			const DataType	vr = sfr [i] - sfi [-i];		// - sfr [nbr_coef - i]
+			const DataType	vi = sfi [i] + sfi [nbr_coef - i];
+
+			df2r [i] = vr * c + vi * s;
+			df2i [i] = vi * c - vr * s;
+		}
+
+		coef_index += d_nbr_coef;
+	}
+	while (coef_index < _length);
+}
+
+
+
+template <class DT>
+void	FFTReal <DT>::compute_inverse_pass_3 (DataType df [], const DataType sf []) const
+{
+	assert (df != 0);
+	assert (sf != 0);
+	assert (df != sf);
+
+	const DataType	sqrt2_2 = DataType (SQRT2 * 0.5);
+	long				coef_index = 0;
+	do
+	{
+		df [coef_index] = sf [coef_index] + sf [coef_index + 4];
+		df [coef_index + 4] = sf [coef_index] - sf [coef_index + 4];
+		df [coef_index + 2] = sf [coef_index + 2] * 2;
+		df [coef_index + 6] = sf [coef_index + 6] * 2;
+
+		df [coef_index + 1] = sf [coef_index + 1] + sf [coef_index + 3];
+		df [coef_index + 3] = sf [coef_index + 5] - sf [coef_index + 7];
+
+		const DataType	vr = sf [coef_index + 1] - sf [coef_index + 3];
+		const DataType	vi = sf [coef_index + 5] + sf [coef_index + 7];
+
+		df [coef_index + 5] = (vr + vi) * sqrt2_2;
+		df [coef_index + 7] = (vi - vr) * sqrt2_2;
+
+		coef_index += 8;
+	}
+	while (coef_index < _length);
+}
+
+
+
+template <class DT>
+void	FFTReal <DT>::compute_inverse_pass_1_2 (DataType x [], const DataType sf []) const
+{
+	assert (x != 0);
+	assert (sf != 0);
+	assert (x != sf);
+
+	const long *	bit_rev_lut_ptr = get_br_ptr ();
+	const DataType *	sf2 = sf;
+	long				coef_index = 0;
+	do
+	{
+		{
+			const DataType	b_0 = sf2 [0] + sf2 [2];
+			const DataType	b_2 = sf2 [0] - sf2 [2];
+			const DataType	b_1 = sf2 [1] * 2;
+			const DataType	b_3 = sf2 [3] * 2;
+
+			x [bit_rev_lut_ptr [0]] = b_0 + b_1;
+			x [bit_rev_lut_ptr [1]] = b_0 - b_1;
+			x [bit_rev_lut_ptr [2]] = b_2 + b_3;
+			x [bit_rev_lut_ptr [3]] = b_2 - b_3;
+		}
+		{
+			const DataType	b_0 = sf2 [4] + sf2 [6];
+			const DataType	b_2 = sf2 [4] - sf2 [6];
+			const DataType	b_1 = sf2 [5] * 2;
+			const DataType	b_3 = sf2 [7] * 2;
+
+			x [bit_rev_lut_ptr [4]] = b_0 + b_1;
+			x [bit_rev_lut_ptr [5]] = b_0 - b_1;
+			x [bit_rev_lut_ptr [6]] = b_2 + b_3;
+			x [bit_rev_lut_ptr [7]] = b_2 - b_3;
+		}
+
+		sf2 += 8;
+		coef_index += 8;
+		bit_rev_lut_ptr += 8;
+	}
+	while (coef_index < _length);
+}
+
+
+
+#endif	// FFTReal_CODEHEADER_INCLUDED
+
+#undef FFTReal_CURRENT_CODEHEADER
+
+
+
+/*\\\ EOF \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
diff --git a/demos/spectrum/fftreal/FFTRealFixLen.h b/demos/spectrum/fftreal/FFTRealFixLen.h
new file mode 100644
index 0000000..0b80266
--- /dev/null
+++ b/demos/spectrum/fftreal/FFTRealFixLen.h
@@ -0,0 +1,130 @@
+/*****************************************************************************
+
+        FFTRealFixLen.h
+        Copyright (c) 2005 Laurent de Soras
+
+--- Legal stuff ---
+
+This library is free software; you can redistribute it and/or
+modify it under the terms of the GNU Lesser General Public
+License as published by the Free Software Foundation; either
+version 2.1 of the License, or (at your option) any later version.
+
+This library is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+Lesser General Public License for more details.
+
+You should have received a copy of the GNU Lesser General Public
+License along with this library; if not, write to the Free Software
+Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
+
+*Tab=3***********************************************************************/
+
+
+
+#if ! defined (FFTRealFixLen_HEADER_INCLUDED)
+#define	FFTRealFixLen_HEADER_INCLUDED
+
+#if defined (_MSC_VER)
+	#pragma once
+	#pragma warning (4 : 4250) // "Inherits via dominance."
+#endif
+
+
+
+/*\\\ INCLUDE FILES \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+#include	"Array.h"
+#include	"DynArray.h"
+#include	"FFTRealFixLenParam.h"
+#include	"OscSinCos.h"
+
+
+
+template <int LL2>
+class FFTRealFixLen
+{
+	typedef	int	CompileTimeCheck1 [(LL2 >=  0) ? 1 : -1];
+	typedef	int	CompileTimeCheck2 [(LL2 <= 30) ? 1 : -1];
+
+/*\\\ PUBLIC \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+public:
+
+   typedef	FFTRealFixLenParam::DataType   DataType;
+	typedef	OscSinCos <DataType>	OscType;
+
+	enum {			FFT_LEN_L2	= LL2	};
+	enum {			FFT_LEN		= 1 << FFT_LEN_L2	};
+
+						FFTRealFixLen ();
+
+	inline long		get_length () const;
+	void				do_fft (DataType f [], const DataType x []);
+	void				do_ifft (const DataType f [], DataType x []);
+	void				rescale (DataType x []) const;
+
+
+
+/*\\\ PROTECTED \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+protected:
+
+
+
+/*\\\ PRIVATE \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+private:
+
+	enum {			TRIGO_BD_LIMIT	= FFTRealFixLenParam::TRIGO_BD_LIMIT	};
+
+	enum {			BR_ARR_SIZE_L2	= ((FFT_LEN_L2 - 3) < 0) ? 0 : (FFT_LEN_L2 - 2)	};
+	enum {			BR_ARR_SIZE		= 1 << BR_ARR_SIZE_L2	};
+
+   enum {			TRIGO_BD			=   ((FFT_LEN_L2 - TRIGO_BD_LIMIT) < 0)
+											  ? (int)FFT_LEN_L2
+											  : (int)TRIGO_BD_LIMIT };
+	enum {			TRIGO_TABLE_ARR_SIZE_L2	= (LL2 < 4) ? 0 : (TRIGO_BD - 2)	};
+	enum {			TRIGO_TABLE_ARR_SIZE	= 1 << TRIGO_TABLE_ARR_SIZE_L2	};
+
+	enum {			NBR_TRIGO_OSC			= FFT_LEN_L2 - TRIGO_BD	};
+	enum {			TRIGO_OSC_ARR_SIZE	=	(NBR_TRIGO_OSC > 0) ? NBR_TRIGO_OSC : 1	};
+
+	void				build_br_lut ();
+	void				build_trigo_lut ();
+	void				build_trigo_osc ();
+
+	DynArray <DataType>
+						_buffer;
+	DynArray <long>
+						_br_data;
+	DynArray <DataType>
+						_trigo_data;
+   Array <OscType, TRIGO_OSC_ARR_SIZE>
+						_trigo_osc;
+
+
+
+/*\\\ FORBIDDEN MEMBER FUNCTIONS \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+private:
+
+						FFTRealFixLen (const FFTRealFixLen &other);
+	FFTRealFixLen&	operator = (const FFTRealFixLen &other);
+	bool				operator == (const FFTRealFixLen &other);
+	bool				operator != (const FFTRealFixLen &other);
+
+};	// class FFTRealFixLen
+
+
+
+#include	"FFTRealFixLen.hpp"
+
+
+
+#endif	// FFTRealFixLen_HEADER_INCLUDED
+
+
+
+/*\\\ EOF \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
diff --git a/demos/spectrum/fftreal/FFTRealFixLen.hpp b/demos/spectrum/fftreal/FFTRealFixLen.hpp
new file mode 100644
index 0000000..6defb00
--- /dev/null
+++ b/demos/spectrum/fftreal/FFTRealFixLen.hpp
@@ -0,0 +1,322 @@
+/*****************************************************************************
+
+        FFTRealFixLen.hpp
+        Copyright (c) 2005 Laurent de Soras
+
+--- Legal stuff ---
+
+This library is free software; you can redistribute it and/or
+modify it under the terms of the GNU Lesser General Public
+License as published by the Free Software Foundation; either
+version 2.1 of the License, or (at your option) any later version.
+
+This library is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+Lesser General Public License for more details.
+
+You should have received a copy of the GNU Lesser General Public
+License along with this library; if not, write to the Free Software
+Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
+
+*Tab=3***********************************************************************/
+
+
+
+#if defined (FFTRealFixLen_CURRENT_CODEHEADER)
+	#error Recursive inclusion of FFTRealFixLen code header.
+#endif
+#define	FFTRealFixLen_CURRENT_CODEHEADER
+
+#if ! defined (FFTRealFixLen_CODEHEADER_INCLUDED)
+#define	FFTRealFixLen_CODEHEADER_INCLUDED
+
+
+
+/*\\\ INCLUDE FILES \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+#include	"def.h"
+#include	"FFTRealPassDirect.h"
+#include	"FFTRealPassInverse.h"
+#include	"FFTRealSelect.h"
+
+#include	<cassert>
+#include	<cmath>
+
+namespace std { }
+
+
+
+/*\\\ PUBLIC \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+
+
+template <int LL2>
+FFTRealFixLen <LL2>::FFTRealFixLen ()
+:	_buffer (FFT_LEN)
+,	_br_data (BR_ARR_SIZE)
+,	_trigo_data (TRIGO_TABLE_ARR_SIZE)
+,	_trigo_osc ()
+{
+	build_br_lut ();
+	build_trigo_lut ();
+	build_trigo_osc ();
+}
+
+
+
+template <int LL2>
+long	FFTRealFixLen <LL2>::get_length () const
+{
+	return (FFT_LEN);
+}
+
+
+
+// General case
+template <int LL2>
+void	FFTRealFixLen <LL2>::do_fft (DataType f [], const DataType x [])
+{
+	assert (f != 0);
+	assert (x != 0);
+	assert (x != f);
+	assert (FFT_LEN_L2 >= 3);
+
+	// Do the transform in several passes
+	const DataType	*	cos_ptr = &_trigo_data [0];
+	const long *	br_ptr = &_br_data [0];
+
+	FFTRealPassDirect <FFT_LEN_L2 - 1>::process (
+		FFT_LEN,
+		f,
+		&_buffer [0],
+		x,
+		cos_ptr,
+		TRIGO_TABLE_ARR_SIZE,
+		br_ptr,
+		&_trigo_osc [0]
+	);
+}
+
+// 4-point FFT
+template <>
+void	FFTRealFixLen <2>::do_fft (DataType f [], const DataType x [])
+{
+	assert (f != 0);
+	assert (x != 0);
+	assert (x != f);
+
+	f [1] = x [0] - x [2];
+	f [3] = x [1] - x [3];
+
+	const DataType	b_0 = x [0] + x [2];
+	const DataType	b_2 = x [1] + x [3];
+	
+	f [0] = b_0 + b_2;
+	f [2] = b_0 - b_2;
+}
+
+// 2-point FFT
+template <>
+void	FFTRealFixLen <1>::do_fft (DataType f [], const DataType x [])
+{
+	assert (f != 0);
+	assert (x != 0);
+	assert (x != f);
+
+	f [0] = x [0] + x [1];
+	f [1] = x [0] - x [1];
+}
+
+// 1-point FFT
+template <>
+void	FFTRealFixLen <0>::do_fft (DataType f [], const DataType x [])
+{
+	assert (f != 0);
+	assert (x != 0);
+
+	f [0] = x [0];
+}
+
+
+
+// General case
+template <int LL2>
+void	FFTRealFixLen <LL2>::do_ifft (const DataType f [], DataType x [])
+{
+	assert (f != 0);
+	assert (x != 0);
+	assert (x != f);
+	assert (FFT_LEN_L2 >= 3);
+
+	// Do the transform in several passes
+	DataType *		s_ptr =
+		FFTRealSelect <FFT_LEN_L2 & 1>::sel_bin (&_buffer [0], x);
+	DataType *		d_ptr =
+		FFTRealSelect <FFT_LEN_L2 & 1>::sel_bin (x, &_buffer [0]);
+	const DataType	*	cos_ptr = &_trigo_data [0];
+	const long *	br_ptr = &_br_data [0];
+
+	FFTRealPassInverse <FFT_LEN_L2 - 1>::process (
+		FFT_LEN,
+		d_ptr,
+		s_ptr,
+		f,
+		cos_ptr,
+		TRIGO_TABLE_ARR_SIZE,
+		br_ptr,
+		&_trigo_osc [0]
+	);
+}
+
+// 4-point IFFT
+template <>
+void	FFTRealFixLen <2>::do_ifft (const DataType f [], DataType x [])
+{
+	assert (f != 0);
+	assert (x != 0);
+	assert (x != f);
+
+	const DataType	b_0 = f [0] + f [2];
+	const DataType	b_2 = f [0] - f [2];
+
+	x [0] = b_0 + f [1] * 2;
+	x [2] = b_0 - f [1] * 2;
+	x [1] = b_2 + f [3] * 2;
+	x [3] = b_2 - f [3] * 2;
+}
+
+// 2-point IFFT
+template <>
+void	FFTRealFixLen <1>::do_ifft (const DataType f [], DataType x [])
+{
+	assert (f != 0);
+	assert (x != 0);
+	assert (x != f);
+
+	x [0] = f [0] + f [1];
+	x [1] = f [0] - f [1];
+}
+
+// 1-point IFFT
+template <>
+void	FFTRealFixLen <0>::do_ifft (const DataType f [], DataType x [])
+{
+	assert (f != 0);
+	assert (x != 0);
+	assert (x != f);
+
+	x [0] = f [0];
+}
+
+
+
+
+template <int LL2>
+void	FFTRealFixLen <LL2>::rescale (DataType x []) const
+{
+	assert (x != 0);
+
+	const DataType	mul = DataType (1.0 / FFT_LEN);
+
+	if (FFT_LEN < 4)
+	{
+		long				i = FFT_LEN - 1;
+		do
+		{
+			x [i] *= mul;
+			--i;
+		}
+		while (i >= 0);
+	}
+
+	else
+	{
+		assert ((FFT_LEN & 3) == 0);
+
+		// Could be optimized with SIMD instruction sets (needs alignment check)
+		long				i = FFT_LEN - 4;
+		do
+		{
+			x [i + 0] *= mul;
+			x [i + 1] *= mul;
+			x [i + 2] *= mul;
+			x [i + 3] *= mul;
+			i -= 4;
+		}
+		while (i >= 0);
+	}
+}
+
+
+
+/*\\\ PROTECTED \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+
+
+/*\\\ PRIVATE \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+
+
+template <int LL2>
+void	FFTRealFixLen <LL2>::build_br_lut ()
+{
+	_br_data [0] = 0;
+	for (long cnt = 1; cnt < BR_ARR_SIZE; ++cnt)
+	{
+		long				index = cnt << 2;
+		long				br_index = 0;
+
+		int				bit_cnt = FFT_LEN_L2;
+		do
+		{
+			br_index <<= 1;
+			br_index += (index & 1);
+			index >>= 1;
+
+			-- bit_cnt;
+		}
+		while (bit_cnt > 0);
+
+		_br_data [cnt] = br_index;
+	}
+}
+
+
+
+template <int LL2>
+void	FFTRealFixLen <LL2>::build_trigo_lut ()
+{
+	const double	mul = (0.5 * PI) / TRIGO_TABLE_ARR_SIZE;
+	for (long i = 0; i < TRIGO_TABLE_ARR_SIZE; ++ i)
+	{
+		using namespace std;
+
+		_trigo_data [i] = DataType (cos (i * mul));
+	}
+}
+
+
+
+template <int LL2>
+void	FFTRealFixLen <LL2>::build_trigo_osc ()
+{
+	for (int i = 0; i < NBR_TRIGO_OSC; ++i)
+	{
+		OscType &		osc = _trigo_osc [i];
+
+		const long		len = static_cast <long> (TRIGO_TABLE_ARR_SIZE) << (i + 1);
+		const double	mul = (0.5 * PI) / len;
+		osc.set_step (mul);
+	}
+}
+
+
+
+#endif	// FFTRealFixLen_CODEHEADER_INCLUDED
+
+#undef FFTRealFixLen_CURRENT_CODEHEADER
+
+
+
+/*\\\ EOF \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
diff --git a/demos/spectrum/fftreal/FFTRealFixLenParam.h b/demos/spectrum/fftreal/FFTRealFixLenParam.h
new file mode 100644
index 0000000..163c083
--- /dev/null
+++ b/demos/spectrum/fftreal/FFTRealFixLenParam.h
@@ -0,0 +1,93 @@
+/*****************************************************************************
+
+        FFTRealFixLenParam.h
+        Copyright (c) 2005 Laurent de Soras
+
+--- Legal stuff ---
+
+This library is free software; you can redistribute it and/or
+modify it under the terms of the GNU Lesser General Public
+License as published by the Free Software Foundation; either
+version 2.1 of the License, or (at your option) any later version.
+
+This library is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+Lesser General Public License for more details.
+
+You should have received a copy of the GNU Lesser General Public
+License along with this library; if not, write to the Free Software
+Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
+
+*Tab=3***********************************************************************/
+
+
+
+#if ! defined (FFTRealFixLenParam_HEADER_INCLUDED)
+#define	FFTRealFixLenParam_HEADER_INCLUDED
+
+#if defined (_MSC_VER)
+	#pragma once
+	#pragma warning (4 : 4250) // "Inherits via dominance."
+#endif
+
+
+
+/*\\\ INCLUDE FILES \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+
+
+class FFTRealFixLenParam
+{
+
+/*\\\ PUBLIC \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+public:
+
+   // Over this bit depth, we use direct calculation for sin/cos
+   enum {	      TRIGO_BD_LIMIT	= 12  };
+
+	typedef	float	DataType;
+
+
+
+/*\\\ PROTECTED \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+protected:
+
+
+
+/*\\\ PRIVATE \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+private:
+
+
+
+/*\\\ FORBIDDEN MEMBER FUNCTIONS \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+private:
+
+#if 0	// To avoid GCC warning:
+		// All member functions in class 'FFTRealFixLenParam' are private
+						FFTRealFixLenParam ();
+						~FFTRealFixLenParam ();
+						FFTRealFixLenParam (const FFTRealFixLenParam &other);
+	FFTRealFixLenParam &
+						operator = (const FFTRealFixLenParam &other);
+	bool				operator == (const FFTRealFixLenParam &other);
+	bool				operator != (const FFTRealFixLenParam &other);
+#endif
+
+};	// class FFTRealFixLenParam
+
+
+
+//#include	"FFTRealFixLenParam.hpp"
+
+
+
+#endif	// FFTRealFixLenParam_HEADER_INCLUDED
+
+
+
+/*\\\ EOF \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
diff --git a/demos/spectrum/fftreal/FFTRealPassDirect.h b/demos/spectrum/fftreal/FFTRealPassDirect.h
new file mode 100644
index 0000000..7d19c02
--- /dev/null
+++ b/demos/spectrum/fftreal/FFTRealPassDirect.h
@@ -0,0 +1,96 @@
+/*****************************************************************************
+
+        FFTRealPassDirect.h
+        Copyright (c) 2005 Laurent de Soras
+
+--- Legal stuff ---
+
+This library is free software; you can redistribute it and/or
+modify it under the terms of the GNU Lesser General Public
+License as published by the Free Software Foundation; either
+version 2.1 of the License, or (at your option) any later version.
+
+This library is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+Lesser General Public License for more details.
+
+You should have received a copy of the GNU Lesser General Public
+License along with this library; if not, write to the Free Software
+Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
+
+*Tab=3***********************************************************************/
+
+
+
+#if ! defined (FFTRealPassDirect_HEADER_INCLUDED)
+#define	FFTRealPassDirect_HEADER_INCLUDED
+
+#if defined (_MSC_VER)
+	#pragma once
+	#pragma warning (4 : 4250) // "Inherits via dominance."
+#endif
+
+
+
+/*\\\ INCLUDE FILES \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+#include	"def.h"
+#include	"FFTRealFixLenParam.h"
+#include	"OscSinCos.h"
+
+
+
+template <int PASS>
+class FFTRealPassDirect
+{
+
+/*\\\ PUBLIC \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+public:
+
+   typedef	FFTRealFixLenParam::DataType	DataType;
+	typedef	OscSinCos <DataType>	OscType;
+
+	FORCEINLINE static void
+						process (long len, DataType dest_ptr [], DataType src_ptr [], const DataType x_ptr [], const DataType cos_ptr [], long cos_len, const long br_ptr [], OscType osc_list []);
+
+
+
+/*\\\ PROTECTED \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+protected:
+
+
+
+/*\\\ PRIVATE \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+private:
+
+
+
+/*\\\ FORBIDDEN MEMBER FUNCTIONS \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+private:
+
+						FFTRealPassDirect ();
+						~FFTRealPassDirect ();
+						FFTRealPassDirect (const FFTRealPassDirect &other);
+	FFTRealPassDirect &
+						operator = (const FFTRealPassDirect &other);
+	bool				operator == (const FFTRealPassDirect &other);
+	bool				operator != (const FFTRealPassDirect &other);
+
+};	// class FFTRealPassDirect
+
+
+
+#include	"FFTRealPassDirect.hpp"
+
+
+
+#endif	// FFTRealPassDirect_HEADER_INCLUDED
+
+
+
+/*\\\ EOF \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
diff --git a/demos/spectrum/fftreal/FFTRealPassDirect.hpp b/demos/spectrum/fftreal/FFTRealPassDirect.hpp
new file mode 100644
index 0000000..db9d568
--- /dev/null
+++ b/demos/spectrum/fftreal/FFTRealPassDirect.hpp
@@ -0,0 +1,204 @@
+/*****************************************************************************
+
+        FFTRealPassDirect.hpp
+        Copyright (c) 2005 Laurent de Soras
+
+--- Legal stuff ---
+
+This library is free software; you can redistribute it and/or
+modify it under the terms of the GNU Lesser General Public
+License as published by the Free Software Foundation; either
+version 2.1 of the License, or (at your option) any later version.
+
+This library is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+Lesser General Public License for more details.
+
+You should have received a copy of the GNU Lesser General Public
+License along with this library; if not, write to the Free Software
+Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
+
+*Tab=3***********************************************************************/
+
+
+
+#if defined (FFTRealPassDirect_CURRENT_CODEHEADER)
+	#error Recursive inclusion of FFTRealPassDirect code header.
+#endif
+#define	FFTRealPassDirect_CURRENT_CODEHEADER
+
+#if ! defined (FFTRealPassDirect_CODEHEADER_INCLUDED)
+#define	FFTRealPassDirect_CODEHEADER_INCLUDED
+
+
+
+/*\\\ INCLUDE FILES \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+#include	"FFTRealUseTrigo.h"
+
+
+
+/*\\\ PUBLIC \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+
+
+template <>
+void	FFTRealPassDirect <1>::process (long len, DataType dest_ptr [], DataType src_ptr [], const DataType x_ptr [], const DataType cos_ptr [], long cos_len, const long br_ptr [], OscType osc_list [])
+{
+	// First and second pass at once
+	const long		qlen = len >> 2;
+
+	long				coef_index = 0;
+	do
+	{
+		// To do: unroll the loop (2x).
+		const long		ri_0 = br_ptr [coef_index >> 2];
+		const long		ri_1 = ri_0 + 2 * qlen;	// bit_rev_lut_ptr [coef_index + 1];
+		const long		ri_2 = ri_0 + 1 * qlen;	// bit_rev_lut_ptr [coef_index + 2];
+		const long		ri_3 = ri_0 + 3 * qlen;	// bit_rev_lut_ptr [coef_index + 3];
+
+		DataType	* const	df2 = dest_ptr + coef_index;
+		df2 [1] = x_ptr [ri_0] - x_ptr [ri_1];
+		df2 [3] = x_ptr [ri_2] - x_ptr [ri_3];
+
+		const DataType	sf_0 = x_ptr [ri_0] + x_ptr [ri_1];
+		const DataType	sf_2 = x_ptr [ri_2] + x_ptr [ri_3];
+
+		df2 [0] = sf_0 + sf_2;
+		df2 [2] = sf_0 - sf_2;
+
+		coef_index += 4;
+	}
+	while (coef_index < len);
+}
+
+template <>
+void	FFTRealPassDirect <2>::process (long len, DataType dest_ptr [], DataType src_ptr [], const DataType x_ptr [], const DataType cos_ptr [], long cos_len, const long br_ptr [], OscType osc_list [])
+{
+	// Executes "previous" passes first. Inverts source and destination buffers
+	FFTRealPassDirect <1>::process (
+		len,
+		src_ptr,
+		dest_ptr,
+		x_ptr,
+		cos_ptr,
+		cos_len,
+		br_ptr,
+		osc_list
+	);
+
+	// Third pass
+	const DataType	sqrt2_2 = DataType (SQRT2 * 0.5);
+
+	long				coef_index = 0;
+	do
+	{
+		dest_ptr [coef_index    ] = src_ptr [coef_index] + src_ptr [coef_index + 4];
+		dest_ptr [coef_index + 4] = src_ptr [coef_index] - src_ptr [coef_index + 4];
+		dest_ptr [coef_index + 2] = src_ptr [coef_index + 2];
+		dest_ptr [coef_index + 6] = src_ptr [coef_index + 6];
+
+		DataType			v;
+
+		v = (src_ptr [coef_index + 5] - src_ptr [coef_index + 7]) * sqrt2_2;
+		dest_ptr [coef_index + 1] = src_ptr [coef_index + 1] + v;
+		dest_ptr [coef_index + 3] = src_ptr [coef_index + 1] - v;
+
+		v = (src_ptr [coef_index + 5] + src_ptr [coef_index + 7]) * sqrt2_2;
+		dest_ptr [coef_index + 5] = v + src_ptr [coef_index + 3];
+		dest_ptr [coef_index + 7] = v - src_ptr [coef_index + 3];
+
+		coef_index += 8;
+	}
+	while (coef_index < len);
+}
+
+template <int PASS>
+void	FFTRealPassDirect <PASS>::process (long len, DataType dest_ptr [], DataType src_ptr [], const DataType x_ptr [], const DataType cos_ptr [], long cos_len, const long br_ptr [], OscType osc_list [])
+{
+	// Executes "previous" passes first. Inverts source and destination buffers
+	FFTRealPassDirect <PASS - 1>::process (
+		len,
+		src_ptr,
+		dest_ptr,
+		x_ptr,
+		cos_ptr,
+		cos_len,
+		br_ptr,
+		osc_list
+	);
+
+	const long		dist = 1L << (PASS - 1);
+	const long		c1_r = 0;
+	const long		c1_i = dist;
+	const long		c2_r = dist * 2;
+	const long		c2_i = dist * 3;
+	const long		cend = dist * 4;
+	const long		table_step = cos_len >> (PASS - 1);
+
+   enum {	TRIGO_OSC		= PASS - FFTRealFixLenParam::TRIGO_BD_LIMIT	};
+	enum {	TRIGO_DIRECT	= (TRIGO_OSC >= 0) ? 1 : 0	};
+
+	long				coef_index = 0;
+	do
+	{
+		const DataType	* const	sf = src_ptr + coef_index;
+		DataType			* const	df = dest_ptr + coef_index;
+
+		// Extreme coefficients are always real
+		df [c1_r] = sf [c1_r] + sf [c2_r];
+		df [c2_r] = sf [c1_r] - sf [c2_r];
+		df [c1_i] = sf [c1_i];
+		df [c2_i] = sf [c2_i];
+
+		FFTRealUseTrigo <TRIGO_DIRECT>::prepare (osc_list [TRIGO_OSC]);
+
+		// Others are conjugate complex numbers
+		for (long i = 1; i < dist; ++ i)
+		{
+			DataType			c;
+			DataType			s;
+			FFTRealUseTrigo <TRIGO_DIRECT>::iterate (
+				osc_list [TRIGO_OSC],
+				c,
+				s,
+				cos_ptr,
+				i * table_step,
+				(dist - i) * table_step
+			);
+
+			const DataType	sf_r_i = sf [c1_r + i];
+			const DataType	sf_i_i = sf [c1_i + i];
+
+			const DataType	v1 = sf [c2_r + i] * c - sf [c2_i + i] * s;
+			df [c1_r + i] = sf_r_i + v1;
+			df [c2_r - i] = sf_r_i - v1;
+
+			const DataType	v2 = sf [c2_r + i] * s + sf [c2_i + i] * c;
+			df [c2_r + i] = v2 + sf_i_i;
+			df [cend - i] = v2 - sf_i_i;
+		}
+
+		coef_index += cend;
+	}
+	while (coef_index < len);
+}
+
+
+
+/*\\\ PROTECTED \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+
+
+/*\\\ PRIVATE \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+
+
+#endif	// FFTRealPassDirect_CODEHEADER_INCLUDED
+
+#undef FFTRealPassDirect_CURRENT_CODEHEADER
+
+
+
+/*\\\ EOF \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
diff --git a/demos/spectrum/fftreal/FFTRealPassInverse.h b/demos/spectrum/fftreal/FFTRealPassInverse.h
new file mode 100644
index 0000000..2de8952
--- /dev/null
+++ b/demos/spectrum/fftreal/FFTRealPassInverse.h
@@ -0,0 +1,101 @@
+/*****************************************************************************
+
+        FFTRealPassInverse.h
+        Copyright (c) 2005 Laurent de Soras
+
+--- Legal stuff ---
+
+This library is free software; you can redistribute it and/or
+modify it under the terms of the GNU Lesser General Public
+License as published by the Free Software Foundation; either
+version 2.1 of the License, or (at your option) any later version.
+
+This library is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+Lesser General Public License for more details.
+
+You should have received a copy of the GNU Lesser General Public
+License along with this library; if not, write to the Free Software
+Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
+
+*Tab=3***********************************************************************/
+
+
+
+#if ! defined (FFTRealPassInverse_HEADER_INCLUDED)
+#define	FFTRealPassInverse_HEADER_INCLUDED
+
+#if defined (_MSC_VER)
+	#pragma once
+	#pragma warning (4 : 4250) // "Inherits via dominance."
+#endif
+
+
+
+/*\\\ INCLUDE FILES \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+#include	"def.h"
+#include	"FFTRealFixLenParam.h"
+#include	"OscSinCos.h"
+
+
+
+
+template <int PASS>
+class FFTRealPassInverse
+{
+
+/*\\\ PUBLIC \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+public:
+
+   typedef	FFTRealFixLenParam::DataType	DataType;
+	typedef	OscSinCos <DataType>	OscType;
+
+	FORCEINLINE static void
+						process (long len, DataType dest_ptr [], DataType src_ptr [], const DataType f_ptr [], const DataType cos_ptr [], long cos_len, const long br_ptr [], OscType osc_list []);
+	FORCEINLINE static void
+						process_rec (long len, DataType dest_ptr [], DataType src_ptr [], const DataType cos_ptr [], long cos_len, const long br_ptr [], OscType osc_list []);
+	FORCEINLINE static void
+						process_internal (long len, DataType dest_ptr [], const DataType src_ptr [], const DataType cos_ptr [], long cos_len, const long br_ptr [], OscType osc_list []);
+
+
+
+/*\\\ PROTECTED \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+protected:
+
+
+
+/*\\\ PRIVATE \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+private:
+
+
+
+/*\\\ FORBIDDEN MEMBER FUNCTIONS \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+private:
+
+						FFTRealPassInverse ();
+						~FFTRealPassInverse ();
+						FFTRealPassInverse (const FFTRealPassInverse &other);
+	FFTRealPassInverse &
+						operator = (const FFTRealPassInverse &other);
+	bool				operator == (const FFTRealPassInverse &other);
+	bool				operator != (const FFTRealPassInverse &other);
+
+};	// class FFTRealPassInverse
+
+
+
+#include	"FFTRealPassInverse.hpp"
+
+
+
+#endif	// FFTRealPassInverse_HEADER_INCLUDED
+
+
+
+/*\\\ EOF \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
diff --git a/demos/spectrum/fftreal/FFTRealPassInverse.hpp b/demos/spectrum/fftreal/FFTRealPassInverse.hpp
new file mode 100644
index 0000000..5737546
--- /dev/null
+++ b/demos/spectrum/fftreal/FFTRealPassInverse.hpp
@@ -0,0 +1,229 @@
+/*****************************************************************************
+
+        FFTRealPassInverse.hpp
+        Copyright (c) 2005 Laurent de Soras
+
+--- Legal stuff ---
+
+This library is free software; you can redistribute it and/or
+modify it under the terms of the GNU Lesser General Public
+License as published by the Free Software Foundation; either
+version 2.1 of the License, or (at your option) any later version.
+
+This library is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+Lesser General Public License for more details.
+
+You should have received a copy of the GNU Lesser General Public
+License along with this library; if not, write to the Free Software
+Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
+
+*Tab=3***********************************************************************/
+
+
+
+#if defined (FFTRealPassInverse_CURRENT_CODEHEADER)
+	#error Recursive inclusion of FFTRealPassInverse code header.
+#endif
+#define	FFTRealPassInverse_CURRENT_CODEHEADER
+
+#if ! defined (FFTRealPassInverse_CODEHEADER_INCLUDED)
+#define	FFTRealPassInverse_CODEHEADER_INCLUDED
+
+
+
+/*\\\ INCLUDE FILES \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+#include	"FFTRealUseTrigo.h"
+
+
+
+/*\\\ PUBLIC \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+
+
+template <int PASS>
+void	FFTRealPassInverse <PASS>::process (long len, DataType dest_ptr [], DataType src_ptr [], const DataType f_ptr [], const DataType cos_ptr [], long cos_len, const long br_ptr [], OscType osc_list [])
+{
+	process_internal (
+		len,
+		dest_ptr,
+		f_ptr,
+		cos_ptr,
+		cos_len,
+		br_ptr,
+		osc_list
+	);
+	FFTRealPassInverse <PASS - 1>::process_rec (
+		len,
+		src_ptr,
+		dest_ptr,
+		cos_ptr,
+		cos_len,
+		br_ptr,
+		osc_list
+	);
+}
+
+
+
+template <int PASS>
+void	FFTRealPassInverse <PASS>::process_rec (long len, DataType dest_ptr [], DataType src_ptr [], const DataType cos_ptr [], long cos_len, const long br_ptr [], OscType osc_list [])
+{
+	process_internal (
+		len,
+		dest_ptr,
+		src_ptr,
+		cos_ptr,
+		cos_len,
+		br_ptr,
+		osc_list
+	);
+	FFTRealPassInverse <PASS - 1>::process_rec (
+		len,
+		src_ptr,
+		dest_ptr,
+		cos_ptr,
+		cos_len,
+		br_ptr,
+		osc_list
+	);
+}
+
+template <>
+void	FFTRealPassInverse <0>::process_rec (long len, DataType dest_ptr [], DataType src_ptr [], const DataType cos_ptr [], long cos_len, const long br_ptr [], OscType osc_list [])
+{
+	// Stops recursion
+}
+
+
+
+template <int PASS>
+void	FFTRealPassInverse <PASS>::process_internal (long len, DataType dest_ptr [], const DataType src_ptr [], const DataType cos_ptr [], long cos_len, const long br_ptr [], OscType osc_list [])
+{
+	const long		dist = 1L << (PASS - 1);
+	const long		c1_r = 0;
+	const long		c1_i = dist;
+	const long		c2_r = dist * 2;
+	const long		c2_i = dist * 3;
+	const long		cend = dist * 4;
+	const long		table_step = cos_len >> (PASS - 1);
+
+   enum {	TRIGO_OSC		= PASS - FFTRealFixLenParam::TRIGO_BD_LIMIT	};
+	enum {	TRIGO_DIRECT	= (TRIGO_OSC >= 0) ? 1 : 0	};
+
+	long				coef_index = 0;
+	do
+	{
+		const DataType	* const	sf = src_ptr + coef_index;
+		DataType			* const	df = dest_ptr + coef_index;
+
+		// Extreme coefficients are always real
+		df [c1_r] = sf [c1_r] + sf [c2_r];
+		df [c2_r] = sf [c1_r] - sf [c2_r];
+		df [c1_i] = sf [c1_i] * 2;
+		df [c2_i] = sf [c2_i] * 2;
+
+		FFTRealUseTrigo <TRIGO_DIRECT>::prepare (osc_list [TRIGO_OSC]);
+
+		// Others are conjugate complex numbers
+		for (long i = 1; i < dist; ++ i)
+		{
+			df [c1_r + i] = sf [c1_r + i] + sf [c2_r - i];
+			df [c1_i + i] = sf [c2_r + i] - sf [cend - i];
+
+			DataType			c;
+			DataType			s;
+			FFTRealUseTrigo <TRIGO_DIRECT>::iterate (
+				osc_list [TRIGO_OSC],
+				c,
+				s,
+				cos_ptr,
+				i * table_step,
+				(dist - i) * table_step
+			);
+
+			const DataType	vr = sf [c1_r + i] - sf [c2_r - i];
+			const DataType	vi = sf [c2_r + i] + sf [cend - i];
+
+			df [c2_r + i] = vr * c + vi * s;
+			df [c2_i + i] = vi * c - vr * s;
+		}
+
+		coef_index += cend;
+	}
+	while (coef_index < len);
+}
+
+template <>
+void	FFTRealPassInverse <2>::process_internal (long len, DataType dest_ptr [], const DataType src_ptr [], const DataType cos_ptr [], long cos_len, const long br_ptr [], OscType osc_list [])
+{
+	// Antepenultimate pass
+	const DataType	sqrt2_2 = DataType (SQRT2 * 0.5);
+
+	long				coef_index = 0;
+	do
+	{
+		dest_ptr [coef_index    ] = src_ptr [coef_index] + src_ptr [coef_index + 4];
+		dest_ptr [coef_index + 4] = src_ptr [coef_index] - src_ptr [coef_index + 4];
+		dest_ptr [coef_index + 2] = src_ptr [coef_index + 2] * 2;
+		dest_ptr [coef_index + 6] = src_ptr [coef_index + 6] * 2;
+
+		dest_ptr [coef_index + 1] = src_ptr [coef_index + 1] + src_ptr [coef_index + 3];
+		dest_ptr [coef_index + 3] = src_ptr [coef_index + 5] - src_ptr [coef_index + 7];
+
+		const DataType	vr = src_ptr [coef_index + 1] - src_ptr [coef_index + 3];
+		const DataType	vi = src_ptr [coef_index + 5] + src_ptr [coef_index + 7];
+
+		dest_ptr [coef_index + 5] = (vr + vi) * sqrt2_2;
+		dest_ptr [coef_index + 7] = (vi - vr) * sqrt2_2;
+
+		coef_index += 8;
+	}
+	while (coef_index < len);
+}
+
+template <>
+void	FFTRealPassInverse <1>::process_internal (long len, DataType dest_ptr [], const DataType src_ptr [], const DataType cos_ptr [], long cos_len, const long br_ptr [], OscType osc_list [])
+{
+	// Penultimate and last pass at once
+	const long		qlen = len >> 2;
+
+	long				coef_index = 0;
+	do
+	{
+		const long		ri_0 = br_ptr [coef_index >> 2];
+
+		const DataType	b_0 = src_ptr [coef_index    ] + src_ptr [coef_index + 2];
+		const DataType	b_2 = src_ptr [coef_index    ] - src_ptr [coef_index + 2];
+		const DataType	b_1 = src_ptr [coef_index + 1] * 2;
+		const DataType	b_3 = src_ptr [coef_index + 3] * 2;
+
+		dest_ptr [ri_0           ] = b_0 + b_1;
+		dest_ptr [ri_0 + 2 * qlen] = b_0 - b_1;
+		dest_ptr [ri_0 + 1 * qlen] = b_2 + b_3;
+		dest_ptr [ri_0 + 3 * qlen] = b_2 - b_3;
+
+		coef_index += 4;
+	}
+	while (coef_index < len);
+}
+
+
+
+/*\\\ PROTECTED \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+
+
+/*\\\ PRIVATE \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+
+
+#endif	// FFTRealPassInverse_CODEHEADER_INCLUDED
+
+#undef FFTRealPassInverse_CURRENT_CODEHEADER
+
+
+
+/*\\\ EOF \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
diff --git a/demos/spectrum/fftreal/FFTRealSelect.h b/demos/spectrum/fftreal/FFTRealSelect.h
new file mode 100644
index 0000000..bd722d4
--- /dev/null
+++ b/demos/spectrum/fftreal/FFTRealSelect.h
@@ -0,0 +1,77 @@
+/*****************************************************************************
+
+        FFTRealSelect.h
+        Copyright (c) 2005 Laurent de Soras
+
+--- Legal stuff ---
+
+This library is free software; you can redistribute it and/or
+modify it under the terms of the GNU Lesser General Public
+License as published by the Free Software Foundation; either
+version 2.1 of the License, or (at your option) any later version.
+
+This library is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+Lesser General Public License for more details.
+
+You should have received a copy of the GNU Lesser General Public
+License along with this library; if not, write to the Free Software
+Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
+
+*Tab=3***********************************************************************/
+
+
+
+#if ! defined (FFTRealSelect_HEADER_INCLUDED)
+#define	FFTRealSelect_HEADER_INCLUDED
+
+#if defined (_MSC_VER)
+	#pragma once
+#endif
+
+
+
+/*\\\ INCLUDE FILES \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+#include	"def.h"
+
+
+
+template <int P>
+class FFTRealSelect
+{
+
+/*\\\ PUBLIC \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+public:
+
+	FORCEINLINE static float *
+						sel_bin (float *e_ptr, float *o_ptr);
+
+
+
+/*\\\ FORBIDDEN MEMBER FUNCTIONS \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+private:
+
+						FFTRealSelect ();
+						~FFTRealSelect ();
+						FFTRealSelect (const FFTRealSelect &other);
+	FFTRealSelect&	operator = (const FFTRealSelect &other);
+	bool				operator == (const FFTRealSelect &other);
+	bool				operator != (const FFTRealSelect &other);
+
+};	// class FFTRealSelect
+
+
+
+#include	"FFTRealSelect.hpp"
+
+
+
+#endif	// FFTRealSelect_HEADER_INCLUDED
+
+
+
+/*\\\ EOF \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
diff --git a/demos/spectrum/fftreal/FFTRealSelect.hpp b/demos/spectrum/fftreal/FFTRealSelect.hpp
new file mode 100644
index 0000000..9ddf586
--- /dev/null
+++ b/demos/spectrum/fftreal/FFTRealSelect.hpp
@@ -0,0 +1,62 @@
+/*****************************************************************************
+
+        FFTRealSelect.hpp
+        Copyright (c) 2005 Laurent de Soras
+
+--- Legal stuff ---
+
+This library is free software; you can redistribute it and/or
+modify it under the terms of the GNU Lesser General Public
+License as published by the Free Software Foundation; either
+version 2.1 of the License, or (at your option) any later version.
+
+This library is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+Lesser General Public License for more details.
+
+You should have received a copy of the GNU Lesser General Public
+License along with this library; if not, write to the Free Software
+Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
+
+*Tab=3***********************************************************************/
+
+
+
+#if defined (FFTRealSelect_CURRENT_CODEHEADER)
+	#error Recursive inclusion of FFTRealSelect code header.
+#endif
+#define	FFTRealSelect_CURRENT_CODEHEADER
+
+#if ! defined (FFTRealSelect_CODEHEADER_INCLUDED)
+#define	FFTRealSelect_CODEHEADER_INCLUDED
+
+
+
+/*\\\ PUBLIC \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+
+
+template <int P>
+float *	FFTRealSelect <P>::sel_bin (float *e_ptr, float *o_ptr)
+{
+	return (o_ptr);
+}
+
+
+
+template <>
+float *	FFTRealSelect <0>::sel_bin (float *e_ptr, float *o_ptr)
+{
+	return (e_ptr);
+}
+
+
+
+#endif	// FFTRealSelect_CODEHEADER_INCLUDED
+
+#undef FFTRealSelect_CURRENT_CODEHEADER
+
+
+
+/*\\\ EOF \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
diff --git a/demos/spectrum/fftreal/FFTRealUseTrigo.h b/demos/spectrum/fftreal/FFTRealUseTrigo.h
new file mode 100644
index 0000000..c4368ee
--- /dev/null
+++ b/demos/spectrum/fftreal/FFTRealUseTrigo.h
@@ -0,0 +1,101 @@
+/*****************************************************************************
+
+        FFTRealUseTrigo.h
+        Copyright (c) 2005 Laurent de Soras
+
+Template parameters:
+	- ALGO: algorithm choice. 0 = table, other = oscillator
+
+--- Legal stuff ---
+
+This library is free software; you can redistribute it and/or
+modify it under the terms of the GNU Lesser General Public
+License as published by the Free Software Foundation; either
+version 2.1 of the License, or (at your option) any later version.
+
+This library is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+Lesser General Public License for more details.
+
+You should have received a copy of the GNU Lesser General Public
+License along with this library; if not, write to the Free Software
+Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
+
+*Tab=3***********************************************************************/
+
+
+
+#if ! defined (FFTRealUseTrigo_HEADER_INCLUDED)
+#define	FFTRealUseTrigo_HEADER_INCLUDED
+
+#if defined (_MSC_VER)
+	#pragma once
+	#pragma warning (4 : 4250) // "Inherits via dominance."
+#endif
+
+
+
+/*\\\ INCLUDE FILES \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+#include	"def.h"
+#include	"FFTRealFixLenParam.h"
+#include	"OscSinCos.h"
+
+
+
+template <int ALGO>
+class FFTRealUseTrigo
+{
+
+/*\\\ PUBLIC \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+public:
+
+   typedef	FFTRealFixLenParam::DataType	DataType;
+	typedef	OscSinCos <DataType>	OscType;
+
+	FORCEINLINE static void
+						prepare (OscType &osc);
+	FORCEINLINE	static void
+						iterate (OscType &osc, DataType &c, DataType &s, const DataType cos_ptr [], long index_c, long index_s);
+
+
+
+/*\\\ PROTECTED \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+protected:
+
+
+
+/*\\\ PRIVATE \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+private:
+
+
+
+/*\\\ FORBIDDEN MEMBER FUNCTIONS \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+private:
+
+						FFTRealUseTrigo ();
+						~FFTRealUseTrigo ();
+						FFTRealUseTrigo (const FFTRealUseTrigo &other);
+	FFTRealUseTrigo &
+						operator = (const FFTRealUseTrigo &other);
+	bool				operator == (const FFTRealUseTrigo &other);
+	bool				operator != (const FFTRealUseTrigo &other);
+
+};	// class FFTRealUseTrigo
+
+
+
+#include	"FFTRealUseTrigo.hpp"
+
+
+
+#endif	// FFTRealUseTrigo_HEADER_INCLUDED
+
+
+
+/*\\\ EOF \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
diff --git a/demos/spectrum/fftreal/FFTRealUseTrigo.hpp b/demos/spectrum/fftreal/FFTRealUseTrigo.hpp
new file mode 100644
index 0000000..aa968b8
--- /dev/null
+++ b/demos/spectrum/fftreal/FFTRealUseTrigo.hpp
@@ -0,0 +1,91 @@
+/*****************************************************************************
+
+        FFTRealUseTrigo.hpp
+        Copyright (c) 2005 Laurent de Soras
+
+--- Legal stuff ---
+
+This library is free software; you can redistribute it and/or
+modify it under the terms of the GNU Lesser General Public
+License as published by the Free Software Foundation; either
+version 2.1 of the License, or (at your option) any later version.
+
+This library is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+Lesser General Public License for more details.
+
+You should have received a copy of the GNU Lesser General Public
+License along with this library; if not, write to the Free Software
+Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
+
+*Tab=3***********************************************************************/
+
+
+
+#if defined (FFTRealUseTrigo_CURRENT_CODEHEADER)
+	#error Recursive inclusion of FFTRealUseTrigo code header.
+#endif
+#define	FFTRealUseTrigo_CURRENT_CODEHEADER
+
+#if ! defined (FFTRealUseTrigo_CODEHEADER_INCLUDED)
+#define	FFTRealUseTrigo_CODEHEADER_INCLUDED
+
+
+
+/*\\\ INCLUDE FILES \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+#include	"OscSinCos.h"
+
+
+
+/*\\\ PUBLIC \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+
+
+template <int ALGO>
+void	FFTRealUseTrigo <ALGO>::prepare (OscType &osc)
+{
+	osc.clear_buffers ();
+}
+
+template <>
+void	FFTRealUseTrigo <0>::prepare (OscType &osc)
+{
+	// Nothing
+}
+
+
+
+template <int ALGO>
+void	FFTRealUseTrigo <ALGO>::iterate (OscType &osc, DataType &c, DataType &s, const DataType cos_ptr [], long index_c, long index_s)
+{
+	osc.step ();
+	c = osc.get_cos ();
+	s = osc.get_sin ();
+}
+
+template <>
+void	FFTRealUseTrigo <0>::iterate (OscType &osc, DataType &c, DataType &s, const DataType cos_ptr [], long index_c, long index_s)
+{
+	c = cos_ptr [index_c];
+	s = cos_ptr [index_s];
+}
+
+
+
+/*\\\ PROTECTED \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+
+
+/*\\\ PRIVATE \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+
+
+#endif	// FFTRealUseTrigo_CODEHEADER_INCLUDED
+
+#undef FFTRealUseTrigo_CURRENT_CODEHEADER
+
+
+
+/*\\\ EOF \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
diff --git a/demos/spectrum/fftreal/OscSinCos.h b/demos/spectrum/fftreal/OscSinCos.h
new file mode 100644
index 0000000..775fc14
--- /dev/null
+++ b/demos/spectrum/fftreal/OscSinCos.h
@@ -0,0 +1,106 @@
+/*****************************************************************************
+
+        OscSinCos.h
+        Copyright (c) 2005 Laurent de Soras
+
+--- Legal stuff ---
+
+This library is free software; you can redistribute it and/or
+modify it under the terms of the GNU Lesser General Public
+License as published by the Free Software Foundation; either
+version 2.1 of the License, or (at your option) any later version.
+
+This library is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+Lesser General Public License for more details.
+
+You should have received a copy of the GNU Lesser General Public
+License along with this library; if not, write to the Free Software
+Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
+
+*Tab=3***********************************************************************/
+
+
+
+#if ! defined (OscSinCos_HEADER_INCLUDED)
+#define	OscSinCos_HEADER_INCLUDED
+
+#if defined (_MSC_VER)
+	#pragma once
+	#pragma warning (4 : 4250) // "Inherits via dominance."
+#endif
+
+
+
+/*\\\ INCLUDE FILES \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+#include	"def.h"
+
+
+
+template <class T>
+class OscSinCos
+{
+
+/*\\\ PUBLIC \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+public:
+
+	typedef	T	DataType;
+
+						OscSinCos ();
+
+	FORCEINLINE void
+						set_step (double angle_rad);
+
+	FORCEINLINE DataType
+						get_cos () const;
+	FORCEINLINE DataType
+						get_sin () const;
+	FORCEINLINE void
+						step ();
+	FORCEINLINE void
+						clear_buffers ();
+
+
+
+/*\\\ PROTECTED \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+protected:
+
+
+
+/*\\\ PRIVATE \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+private:
+
+	DataType			_pos_cos;		// Current phase expressed with sin and cos. [-1 ; 1]
+	DataType			_pos_sin;		// -
+	DataType			_step_cos;		// Phase increment per step, [-1 ; 1]
+	DataType			_step_sin;		// -
+
+
+
+/*\\\ FORBIDDEN MEMBER FUNCTIONS \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+private:
+
+						OscSinCos (const OscSinCos &other);
+	OscSinCos &		operator = (const OscSinCos &other);
+	bool				operator == (const OscSinCos &other);
+	bool				operator != (const OscSinCos &other);
+
+};	// class OscSinCos
+
+
+
+#include	"OscSinCos.hpp"
+
+
+
+#endif	// OscSinCos_HEADER_INCLUDED
+
+
+
+/*\\\ EOF \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
diff --git a/demos/spectrum/fftreal/OscSinCos.hpp b/demos/spectrum/fftreal/OscSinCos.hpp
new file mode 100644
index 0000000..749aef0
--- /dev/null
+++ b/demos/spectrum/fftreal/OscSinCos.hpp
@@ -0,0 +1,122 @@
+/*****************************************************************************
+
+        OscSinCos.hpp
+        Copyright (c) 2005 Laurent de Soras
+
+--- Legal stuff ---
+
+This library is free software; you can redistribute it and/or
+modify it under the terms of the GNU Lesser General Public
+License as published by the Free Software Foundation; either
+version 2.1 of the License, or (at your option) any later version.
+
+This library is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+Lesser General Public License for more details.
+
+You should have received a copy of the GNU Lesser General Public
+License along with this library; if not, write to the Free Software
+Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
+
+*Tab=3***********************************************************************/
+
+
+
+#if defined (OscSinCos_CURRENT_CODEHEADER)
+	#error Recursive inclusion of OscSinCos code header.
+#endif
+#define	OscSinCos_CURRENT_CODEHEADER
+
+#if ! defined (OscSinCos_CODEHEADER_INCLUDED)
+#define	OscSinCos_CODEHEADER_INCLUDED
+
+
+
+/*\\\ INCLUDE FILES \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+#include	<cmath>
+
+namespace std { }
+
+
+
+/*\\\ PUBLIC \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+
+
+template <class T>
+OscSinCos <T>::OscSinCos ()
+:	_pos_cos (1)
+,	_pos_sin (0)
+,	_step_cos (1)
+,	_step_sin (0)
+{
+	// Nothing
+}
+
+
+
+template <class T>
+void	OscSinCos <T>::set_step (double angle_rad)
+{
+	using namespace std;
+
+	_step_cos = static_cast <DataType> (cos (angle_rad));
+	_step_sin = static_cast <DataType> (sin (angle_rad));
+}
+
+
+
+template <class T>
+typename OscSinCos <T>::DataType	OscSinCos <T>::get_cos () const
+{
+	return (_pos_cos);
+}
+
+
+
+template <class T>
+typename OscSinCos <T>::DataType	OscSinCos <T>::get_sin () const
+{
+	return (_pos_sin);
+}
+
+
+
+template <class T>
+void	OscSinCos <T>::step ()
+{
+	const DataType	old_cos = _pos_cos;
+	const DataType	old_sin = _pos_sin;
+
+	_pos_cos = old_cos * _step_cos - old_sin * _step_sin;
+	_pos_sin = old_cos * _step_sin + old_sin * _step_cos;
+}
+
+
+
+template <class T>
+void	OscSinCos <T>::clear_buffers ()
+{
+	_pos_cos = static_cast <DataType> (1);
+	_pos_sin = static_cast <DataType> (0);
+}
+
+
+
+/*\\\ PROTECTED \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+
+
+/*\\\ PRIVATE \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+
+
+#endif	// OscSinCos_CODEHEADER_INCLUDED
+
+#undef OscSinCos_CURRENT_CODEHEADER
+
+
+
+/*\\\ EOF \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
diff --git a/demos/spectrum/fftreal/TestAccuracy.h b/demos/spectrum/fftreal/TestAccuracy.h
new file mode 100644
index 0000000..4b07a6b
--- /dev/null
+++ b/demos/spectrum/fftreal/TestAccuracy.h
@@ -0,0 +1,105 @@
+/*****************************************************************************
+
+        TestAccuracy.h
+        Copyright (c) 2005 Laurent de Soras
+
+--- Legal stuff ---
+
+This library is free software; you can redistribute it and/or
+modify it under the terms of the GNU Lesser General Public
+License as published by the Free Software Foundation; either
+version 2.1 of the License, or (at your option) any later version.
+
+This library is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+Lesser General Public License for more details.
+
+You should have received a copy of the GNU Lesser General Public
+License along with this library; if not, write to the Free Software
+Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
+
+*Tab=3***********************************************************************/
+
+
+
+#if ! defined (TestAccuracy_HEADER_INCLUDED)
+#define	TestAccuracy_HEADER_INCLUDED
+
+#if defined (_MSC_VER)
+	#pragma once
+	#pragma warning (4 : 4250) // "Inherits via dominance."
+#endif
+
+
+
+/*\\\ INCLUDE FILES \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+
+
+template <class FO>
+class TestAccuracy
+{
+
+/*\\\ PUBLIC \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+public:
+
+	typedef	typename FO::DataType	DataType;
+	typedef	long double	BigFloat;	// To get maximum accuracy during intermediate calculations
+
+   static int		perform_test_single_object (FO &fft);
+   static int		perform_test_d (FO &fft, const char *class_name_0);
+   static int		perform_test_i (FO &fft, const char *class_name_0);
+   static int		perform_test_di (FO &fft, const char *class_name_0);
+
+
+
+/*\\\ PROTECTED \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+protected:
+
+
+
+/*\\\ PRIVATE \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+private:
+
+	enum {			NBR_ACC_TESTS	= 10 * 1000 * 1000	};
+   enum {         MAX_NBR_TESTS  = 10000  };
+
+   static void		compute_tf (DataType s [], const DataType x [], long length);
+	static void		compute_itf (DataType x [], const DataType s [], long length);
+	static int		compare_vect_display (const DataType x_ptr [], const DataType y_ptr [], long len, BigFloat &max_err_rel);
+	static BigFloat
+						compute_power (const DataType x_ptr [], long len);
+	static BigFloat
+						compute_power (const DataType x_ptr [], const DataType y_ptr [], long len);
+	static void		compare_vect (const DataType x_ptr [], const DataType y_ptr [], BigFloat &power, long &max_err_pos, long len);
+
+
+
+/*\\\ FORBIDDEN MEMBER FUNCTIONS \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+private:
+
+						TestAccuracy ();
+						~TestAccuracy ();
+						TestAccuracy (const TestAccuracy &other);
+	TestAccuracy &	operator = (const TestAccuracy &other);
+	bool				operator == (const TestAccuracy &other);
+	bool				operator != (const TestAccuracy &other);
+
+};	// class TestAccuracy
+
+
+
+#include	"TestAccuracy.hpp"
+
+
+
+#endif	// TestAccuracy_HEADER_INCLUDED
+
+
+
+/*\\\ EOF \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
diff --git a/demos/spectrum/fftreal/TestAccuracy.hpp b/demos/spectrum/fftreal/TestAccuracy.hpp
new file mode 100644
index 0000000..5c794f7
--- /dev/null
+++ b/demos/spectrum/fftreal/TestAccuracy.hpp
@@ -0,0 +1,472 @@
+/*****************************************************************************
+
+        TestAccuracy.hpp
+        Copyright (c) 2005 Laurent de Soras
+
+--- Legal stuff ---
+
+This library is free software; you can redistribute it and/or
+modify it under the terms of the GNU Lesser General Public
+License as published by the Free Software Foundation; either
+version 2.1 of the License, or (at your option) any later version.
+
+This library is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+Lesser General Public License for more details.
+
+You should have received a copy of the GNU Lesser General Public
+License along with this library; if not, write to the Free Software
+Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
+
+*Tab=3***********************************************************************/
+
+
+
+#if defined (TestAccuracy_CURRENT_CODEHEADER)
+	#error Recursive inclusion of TestAccuracy code header.
+#endif
+#define	TestAccuracy_CURRENT_CODEHEADER
+
+#if ! defined (TestAccuracy_CODEHEADER_INCLUDED)
+#define	TestAccuracy_CODEHEADER_INCLUDED
+
+
+
+/*\\\ INCLUDE FILES \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+#include	"def.h"
+#include	"test_fnc.h"
+#include	"TestWhiteNoiseGen.h"
+
+#include	<typeinfo>
+#include	<vector>
+
+#include	<cmath>
+#include	<cstdio>
+
+
+
+static const double	TestAccuracy_LN10	= 2.3025850929940456840179914546844;
+
+
+
+/*\\\ PUBLIC \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+
+
+template <class FO>
+int	TestAccuracy <FO>::perform_test_single_object (FO &fft)
+{
+	assert (&fft != 0);
+
+	using namespace std;
+
+	int				ret_val = 0;
+
+	const std::type_info &	ti = typeid (fft);
+	const char *	class_name_0 = ti.name ();
+
+	if (ret_val == 0)
+	{
+		ret_val = perform_test_d (fft, class_name_0);
+	}
+	if (ret_val == 0)
+	{
+		ret_val = perform_test_i (fft, class_name_0);
+	}
+	if (ret_val == 0)
+	{
+		ret_val = perform_test_di (fft, class_name_0);
+	}
+
+	if (ret_val == 0)
+	{
+		printf ("\n");
+	}
+
+	return (ret_val);
+}
+
+
+
+template <class FO>
+int	TestAccuracy <FO>::perform_test_d (FO &fft, const char *class_name_0)
+{
+	assert (&fft != 0);
+   assert (class_name_0 != 0);
+
+	using namespace std;
+
+	int				ret_val = 0;
+	const long		len = fft.get_length ();
+   const long     nbr_tests = limit (
+      NBR_ACC_TESTS / len / len,
+      1L,
+      static_cast <long> (MAX_NBR_TESTS)
+   );
+
+	printf ("Testing %s::do_fft () [%ld samples]... ", class_name_0, len);
+	fflush (stdout);
+	TestWhiteNoiseGen <DataType>	noise;
+	std::vector <DataType>	x (len);
+	std::vector <DataType>	s1 (len);
+	std::vector <DataType>	s2 (len);
+	BigFloat			err_avg = 0;
+
+	for (long test = 0; test < nbr_tests && ret_val == 0; ++ test)
+	{
+		noise.generate (&x [0], len);
+		fft.do_fft (&s1 [0], &x [0]);
+		compute_tf (&s2 [0], &x [0], len);
+
+		BigFloat			max_err;
+		compare_vect_display (&s1 [0], &s2 [0], len, max_err);
+		err_avg += max_err;
+	}
+	err_avg /= NBR_ACC_TESTS;
+
+	printf ("done.\n");
+	printf (
+		"Average maximum error: %.6f %% (%f dB)\n",
+		static_cast <double> (err_avg * 100),
+		static_cast <double> ((20 / TestAccuracy_LN10) * log (err_avg))
+	);
+
+	return (ret_val);
+}
+
+
+
+template <class FO>
+int	TestAccuracy <FO>::perform_test_i (FO &fft, const char *class_name_0)
+{
+	assert (&fft != 0);
+   assert (class_name_0 != 0);
+
+	using namespace std;
+
+	int				ret_val = 0;
+	const long		len = fft.get_length ();
+   const long     nbr_tests = limit (
+      NBR_ACC_TESTS / len / len,
+      10L,
+      static_cast <long> (MAX_NBR_TESTS)
+   );
+
+	printf ("Testing %s::do_ifft () [%ld samples]... ", class_name_0, len);
+	fflush (stdout);
+	TestWhiteNoiseGen <DataType>	noise;
+	std::vector <DataType>	s (len);
+	std::vector <DataType>	x1 (len);
+	std::vector <DataType>	x2 (len);
+	BigFloat			err_avg = 0;
+
+	for (long test = 0; test < nbr_tests && ret_val == 0; ++ test)
+	{
+		noise.generate (&s [0], len);
+		fft.do_ifft (&s [0], &x1 [0]);
+		compute_itf (&x2 [0], &s [0], len);
+
+		BigFloat			max_err;
+		compare_vect_display (&x1 [0], &x2 [0], len, max_err);
+		err_avg += max_err;
+	}
+	err_avg /= NBR_ACC_TESTS;
+
+	printf ("done.\n");
+	printf (
+		"Average maximum error: %.6f %% (%f dB)\n",
+		static_cast <double> (err_avg * 100),
+		static_cast <double> ((20 / TestAccuracy_LN10) * log (err_avg))
+	);
+
+	return (ret_val);
+}
+
+
+
+template <class FO>
+int	TestAccuracy <FO>::perform_test_di (FO &fft, const char *class_name_0)
+{
+	assert (&fft != 0);
+   assert (class_name_0 != 0);
+
+	using namespace std;
+
+	int				ret_val = 0;
+	const long		len = fft.get_length ();
+   const long     nbr_tests = limit (
+      NBR_ACC_TESTS / len / len,
+      1L,
+      static_cast <long> (MAX_NBR_TESTS)
+   );
+
+	printf (
+		"Testing %s::do_fft () / do_ifft () / rescale () [%ld samples]... ",
+		class_name_0,
+		len
+	);
+	fflush (stdout);
+	TestWhiteNoiseGen <DataType>	noise;
+	std::vector <DataType>	x (len);
+	std::vector <DataType>	s (len);
+	std::vector <DataType>	y (len);
+	BigFloat			err_avg = 0;
+
+	for (long test = 0; test < nbr_tests && ret_val == 0; ++ test)
+	{
+		noise.generate (&x [0], len);
+		fft.do_fft (&s [0], &x [0]);
+		fft.do_ifft (&s [0], &y [0]);
+		fft.rescale (&y [0]);
+
+		BigFloat			max_err;
+		compare_vect_display (&x [0], &y [0], len, max_err);
+		err_avg += max_err;
+	}
+	err_avg /= NBR_ACC_TESTS;
+
+	printf ("done.\n");
+	printf (
+		"Average maximum error: %.6f %% (%f dB)\n",
+		static_cast <double> (err_avg * 100),
+		static_cast <double> ((20 / TestAccuracy_LN10) * log (err_avg))
+	);
+
+	return (ret_val);
+}
+
+
+
+/*\\\ PROTECTED \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+
+
+/*\\\ PRIVATE \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+
+
+// Positive transform
+template <class FO>
+void	TestAccuracy <FO>::compute_tf (DataType s [], const DataType x [], long length)
+{
+	assert (s != 0);
+	assert (x != 0);
+	assert (length >= 2);
+	assert ((length & 1) == 0);
+
+	const long		nbr_bins = length >> 1;
+
+	// DC and Nyquist
+	BigFloat			dc = 0;
+	BigFloat			ny = 0;
+	for (long pos = 0; pos < length; pos += 2)
+	{
+		const BigFloat	even = x [pos    ];
+		const BigFloat	odd  = x [pos + 1];
+		dc += even + odd;
+		ny += even - odd;
+	}
+	s [0       ] = static_cast <DataType> (dc);
+	s [nbr_bins] = static_cast <DataType> (ny);
+
+	// Regular bins
+	for (long bin = 1; bin < nbr_bins; ++ bin)
+	{
+		BigFloat			sum_r = 0;
+		BigFloat			sum_i = 0;
+
+		const BigFloat	m = bin * static_cast <BigFloat> (2 * PI) / length;
+
+		for (long pos = 0; pos < length; ++pos)
+		{
+			using namespace std;
+
+			const BigFloat	phase = pos * m;
+			const BigFloat	e_r = cos (phase);
+			const BigFloat	e_i = sin (phase);
+
+			sum_r += x [pos] * e_r;
+			sum_i += x [pos] * e_i;
+		}
+
+		s [           bin] = static_cast <DataType> (sum_r);
+		s [nbr_bins + bin] = static_cast <DataType> (sum_i);
+	}
+}
+
+
+
+// Negative transform
+template <class FO>
+void	TestAccuracy <FO>::compute_itf (DataType x [], const DataType s [], long length)
+{
+	assert (s != 0);
+	assert (x != 0);
+	assert (length >= 2);
+	assert ((length & 1) == 0);
+
+	const long		nbr_bins = length >> 1;
+
+	// DC and Nyquist
+	BigFloat			dc = s [0       ];
+	BigFloat			ny = s [nbr_bins];
+
+	// Regular bins
+	for (long pos = 0; pos < length; ++pos)
+	{
+		BigFloat				sum = dc + ny * (1 - 2 * (pos & 1));
+
+		const BigFloat		m = pos * static_cast <BigFloat> (-2 * PI) / length;
+
+		for (long bin = 1; bin < nbr_bins; ++ bin)
+		{
+			using namespace std;
+
+			const BigFloat	phase = bin * m;
+			const BigFloat	e_r = cos (phase);
+			const BigFloat	e_i = sin (phase);
+
+			sum += 2 * (  e_r * s [bin           ]
+			            - e_i * s [bin + nbr_bins]);
+		}
+
+		x [pos] = static_cast <DataType> (sum);
+	}
+}
+
+
+
+template <class FO>
+int	TestAccuracy <FO>::compare_vect_display (const DataType x_ptr [], const DataType y_ptr [], long len, BigFloat &max_err_rel)
+{
+	assert (x_ptr != 0);
+	assert (y_ptr != 0);
+	assert (len > 0);
+	assert (&max_err_rel != 0);
+
+	using namespace std;
+
+	int				ret_val = 0;
+
+	BigFloat			power = compute_power (&x_ptr [0], &y_ptr [0], len);
+	BigFloat			power_dif;
+	long				max_err_pos;
+	compare_vect (&x_ptr [0], &y_ptr [0], power_dif, max_err_pos, len);
+
+	if (power == 0)
+	{
+		power = power_dif;
+	}
+	const BigFloat	power_err_rel = power_dif / power;
+
+	BigFloat	      max_err = 0;
+	max_err_rel = 0;
+	if (max_err_pos >= 0)
+	{
+      max_err = y_ptr [max_err_pos] - x_ptr [max_err_pos];
+		max_err_rel = 2 * fabs (max_err) / (  fabs (y_ptr [max_err_pos])
+		                                    + fabs (x_ptr [max_err_pos]));
+	}
+
+	if (power_err_rel > 0.001)
+	{
+		printf ("Power error  : %f (%.6f %%)\n",
+			static_cast <double> (power_err_rel),
+			static_cast <double> (power_err_rel * 100)
+		);
+		if (max_err_pos >= 0)
+		{
+			printf (
+				"Maximum error: %f - %f = %f (%f)\n",
+				static_cast <double> (y_ptr [max_err_pos]),
+				static_cast <double> (x_ptr [max_err_pos]),
+				static_cast <double> (max_err),
+				static_cast <double> (max_err_pos)
+			);
+		}
+	}
+
+	return (ret_val);
+}
+
+
+
+template <class FO>
+typename TestAccuracy <FO>::BigFloat	TestAccuracy <FO>::compute_power (const DataType x_ptr [], long len)
+{
+	assert (x_ptr != 0);
+	assert (len > 0);
+
+	BigFloat		power = 0;
+	for (long pos = 0; pos < len; ++pos)
+	{
+		const BigFloat	val = x_ptr [pos];
+
+		power += val * val;
+	}
+
+	using namespace std;
+
+	power = sqrt (power) / len;
+
+	return (power);
+}
+
+
+
+template <class FO>
+typename TestAccuracy <FO>::BigFloat	TestAccuracy <FO>::compute_power (const DataType x_ptr [], const DataType y_ptr [], long len)
+{
+	assert (x_ptr != 0);
+	assert (y_ptr != 0);
+	assert (len > 0);
+
+	return ((compute_power (x_ptr, len) + compute_power (y_ptr, len)) * 0.5);
+}
+
+
+
+template <class FO>
+void	TestAccuracy <FO>::compare_vect (const DataType x_ptr [], const DataType y_ptr [], BigFloat &power, long &max_err_pos, long len)
+{
+	assert (x_ptr != 0);
+	assert (y_ptr != 0);
+	assert (len > 0);
+	assert (&power != 0);
+	assert (&max_err_pos != 0);
+
+	power = 0;
+	BigFloat			max_dif2 = 0;
+	max_err_pos = -1;
+
+	for (long pos = 0; pos < len; ++pos)
+	{
+		const BigFloat	x = x_ptr [pos];
+		const BigFloat	y = y_ptr [pos];
+		const BigFloat	dif = y - x;
+		const BigFloat	dif2 = dif * dif;
+
+		power += dif2;
+		if (dif2 > max_dif2)
+		{
+			max_err_pos = pos;
+			max_dif2 = dif2;
+		}
+	}
+
+	using namespace std;
+
+	power = sqrt (power) / len;
+}
+
+
+
+#endif	// TestAccuracy_CODEHEADER_INCLUDED
+
+#undef TestAccuracy_CURRENT_CODEHEADER
+
+
+
+/*\\\ EOF \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
diff --git a/demos/spectrum/fftreal/TestHelperFixLen.h b/demos/spectrum/fftreal/TestHelperFixLen.h
new file mode 100644
index 0000000..ecff96d
--- /dev/null
+++ b/demos/spectrum/fftreal/TestHelperFixLen.h
@@ -0,0 +1,93 @@
+/*****************************************************************************
+
+        TestHelperFixLen.h
+        Copyright (c) 2005 Laurent de Soras
+
+--- Legal stuff ---
+
+This library is free software; you can redistribute it and/or
+modify it under the terms of the GNU Lesser General Public
+License as published by the Free Software Foundation; either
+version 2.1 of the License, or (at your option) any later version.
+
+This library is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+Lesser General Public License for more details.
+
+You should have received a copy of the GNU Lesser General Public
+License along with this library; if not, write to the Free Software
+Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
+
+*Tab=3***********************************************************************/
+
+
+
+#if ! defined (TestHelperFixLen_HEADER_INCLUDED)
+#define	TestHelperFixLen_HEADER_INCLUDED
+
+#if defined (_MSC_VER)
+	#pragma once
+	#pragma warning (4 : 4250) // "Inherits via dominance."
+#endif
+
+
+
+/*\\\ INCLUDE FILES \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+#include	"FFTRealFixLen.h"
+
+
+
+template <int L>
+class TestHelperFixLen
+{
+
+/*\\\ PUBLIC \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+public:
+
+	typedef  FFTRealFixLen <L> FftType;
+
+   static void    perform_test_accuracy (int &ret_val);
+   static void    perform_test_speed (int &ret_val);
+
+
+
+/*\\\ PROTECTED \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+protected:
+
+
+
+/*\\\ PRIVATE \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+private:
+
+
+
+/*\\\ FORBIDDEN MEMBER FUNCTIONS \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+private:
+
+						TestHelperFixLen ();
+						~TestHelperFixLen ();
+						TestHelperFixLen (const TestHelperFixLen &other);
+	TestHelperFixLen &
+						operator = (const TestHelperFixLen &other);
+	bool				operator == (const TestHelperFixLen &other);
+	bool				operator != (const TestHelperFixLen &other);
+
+};	// class TestHelperFixLen
+
+
+
+#include	"TestHelperFixLen.hpp"
+
+
+
+#endif	// TestHelperFixLen_HEADER_INCLUDED
+
+
+
+/*\\\ EOF \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
diff --git a/demos/spectrum/fftreal/TestHelperFixLen.hpp b/demos/spectrum/fftreal/TestHelperFixLen.hpp
new file mode 100644
index 0000000..25048b9
--- /dev/null
+++ b/demos/spectrum/fftreal/TestHelperFixLen.hpp
@@ -0,0 +1,93 @@
+/*****************************************************************************
+
+        TestHelperFixLen.hpp
+        Copyright (c) 2005 Laurent de Soras
+
+--- Legal stuff ---
+
+This library is free software; you can redistribute it and/or
+modify it under the terms of the GNU Lesser General Public
+License as published by the Free Software Foundation; either
+version 2.1 of the License, or (at your option) any later version.
+
+This library is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+Lesser General Public License for more details.
+
+You should have received a copy of the GNU Lesser General Public
+License along with this library; if not, write to the Free Software
+Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
+
+*Tab=3***********************************************************************/
+
+
+
+#if defined (TestHelperFixLen_CURRENT_CODEHEADER)
+	#error Recursive inclusion of TestHelperFixLen code header.
+#endif
+#define	TestHelperFixLen_CURRENT_CODEHEADER
+
+#if ! defined (TestHelperFixLen_CODEHEADER_INCLUDED)
+#define	TestHelperFixLen_CODEHEADER_INCLUDED
+
+
+
+/*\\\ INCLUDE FILES \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+#include	"test_settings.h"
+
+#include	"TestAccuracy.h"
+#if defined (test_settings_SPEED_TEST_ENABLED)
+	#include	"TestSpeed.h"
+#endif
+
+
+
+/*\\\ PUBLIC \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+
+
+template <int L>
+void	TestHelperFixLen <L>::perform_test_accuracy (int &ret_val)
+{
+   if (ret_val == 0)
+   {
+		FftType			fft;
+      ret_val = TestAccuracy <FftType>::perform_test_single_object (fft);
+   }
+}
+
+
+
+template <int L>
+void	TestHelperFixLen <L>::perform_test_speed (int &ret_val)
+{
+#if defined (test_settings_SPEED_TEST_ENABLED)
+
+   if (ret_val == 0)
+   {
+		FftType			fft;
+      ret_val = TestSpeed <FftType>::perform_test_single_object (fft);
+   }
+
+#endif
+}
+
+
+
+/*\\\ PROTECTED \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+
+
+/*\\\ PRIVATE \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+
+
+#endif	// TestHelperFixLen_CODEHEADER_INCLUDED
+
+#undef TestHelperFixLen_CURRENT_CODEHEADER
+
+
+
+/*\\\ EOF \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
diff --git a/demos/spectrum/fftreal/TestHelperNormal.h b/demos/spectrum/fftreal/TestHelperNormal.h
new file mode 100644
index 0000000..a7bff5c
--- /dev/null
+++ b/demos/spectrum/fftreal/TestHelperNormal.h
@@ -0,0 +1,94 @@
+/*****************************************************************************
+
+        TestHelperNormal.h
+        Copyright (c) 2005 Laurent de Soras
+
+--- Legal stuff ---
+
+This library is free software; you can redistribute it and/or
+modify it under the terms of the GNU Lesser General Public
+License as published by the Free Software Foundation; either
+version 2.1 of the License, or (at your option) any later version.
+
+This library is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+Lesser General Public License for more details.
+
+You should have received a copy of the GNU Lesser General Public
+License along with this library; if not, write to the Free Software
+Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
+
+*Tab=3***********************************************************************/
+
+
+
+#if ! defined (TestHelperNormal_HEADER_INCLUDED)
+#define	TestHelperNormal_HEADER_INCLUDED
+
+#if defined (_MSC_VER)
+	#pragma once
+	#pragma warning (4 : 4250) // "Inherits via dominance."
+#endif
+
+
+
+/*\\\ INCLUDE FILES \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+#include	"FFTReal.h"
+
+
+
+template <class DT>
+class TestHelperNormal
+{
+
+/*\\\ PUBLIC \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+public:
+
+	typedef	DT	DataType;
+	typedef	FFTReal <DataType>	FftType;
+
+   static void    perform_test_accuracy (int &ret_val);
+   static void    perform_test_speed (int &ret_val);
+
+
+
+/*\\\ PROTECTED \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+protected:
+
+
+
+/*\\\ PRIVATE \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+private:
+
+
+
+/*\\\ FORBIDDEN MEMBER FUNCTIONS \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+private:
+
+						TestHelperNormal ();
+						~TestHelperNormal ();
+						TestHelperNormal (const TestHelperNormal &other);
+	TestHelperNormal &
+						operator = (const TestHelperNormal &other);
+	bool				operator == (const TestHelperNormal &other);
+	bool				operator != (const TestHelperNormal &other);
+
+};	// class TestHelperNormal
+
+
+
+#include	"TestHelperNormal.hpp"
+
+
+
+#endif	// TestHelperNormal_HEADER_INCLUDED
+
+
+
+/*\\\ EOF \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
diff --git a/demos/spectrum/fftreal/TestHelperNormal.hpp b/demos/spectrum/fftreal/TestHelperNormal.hpp
new file mode 100644
index 0000000..e037696
--- /dev/null
+++ b/demos/spectrum/fftreal/TestHelperNormal.hpp
@@ -0,0 +1,99 @@
+/*****************************************************************************
+
+        TestHelperNormal.hpp
+        Copyright (c) 2005 Laurent de Soras
+
+--- Legal stuff ---
+
+This library is free software; you can redistribute it and/or
+modify it under the terms of the GNU Lesser General Public
+License as published by the Free Software Foundation; either
+version 2.1 of the License, or (at your option) any later version.
+
+This library is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+Lesser General Public License for more details.
+
+You should have received a copy of the GNU Lesser General Public
+License along with this library; if not, write to the Free Software
+Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
+
+*Tab=3***********************************************************************/
+
+
+
+#if defined (TestHelperNormal_CURRENT_CODEHEADER)
+	#error Recursive inclusion of TestHelperNormal code header.
+#endif
+#define	TestHelperNormal_CURRENT_CODEHEADER
+
+#if ! defined (TestHelperNormal_CODEHEADER_INCLUDED)
+#define	TestHelperNormal_CODEHEADER_INCLUDED
+
+
+
+/*\\\ INCLUDE FILES \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+#include	"test_settings.h"
+
+#include	"TestAccuracy.h"
+#if defined (test_settings_SPEED_TEST_ENABLED)
+	#include	"TestSpeed.h"
+#endif
+
+
+
+/*\\\ PUBLIC \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+
+
+template <class DT>
+void	TestHelperNormal <DT>::perform_test_accuracy (int &ret_val)
+{
+	const int		len_arr [] = { 1, 2, 3, 4, 7, 8, 10, 12 };
+	const int		nbr_len = sizeof (len_arr) / sizeof (len_arr [0]);
+	for (int k = 0; k < nbr_len && ret_val == 0; ++k)
+	{
+		const long		len = 1L << (len_arr [k]);
+		FftType			fft (len);
+		ret_val = TestAccuracy <FftType>::perform_test_single_object (fft);
+	}
+}
+
+
+
+template <class DT>
+void	TestHelperNormal <DT>::perform_test_speed (int &ret_val)
+{
+#if defined (test_settings_SPEED_TEST_ENABLED)
+
+	const int		len_arr [] = { 1, 2, 3, 4, 7, 8, 10, 12, 14, 16, 18, 20, 22 };
+	const int		nbr_len = sizeof (len_arr) / sizeof (len_arr [0]);
+	for (int k = 0; k < nbr_len && ret_val == 0; ++k)
+	{
+		const long		len = 1L << (len_arr [k]);
+		FftType			fft (len);
+		ret_val = TestSpeed <FftType>::perform_test_single_object (fft);
+	}
+
+#endif
+}
+
+
+
+/*\\\ PROTECTED \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+
+
+/*\\\ PRIVATE \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+
+
+#endif	// TestHelperNormal_CODEHEADER_INCLUDED
+
+#undef TestHelperNormal_CURRENT_CODEHEADER
+
+
+
+/*\\\ EOF \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
diff --git a/demos/spectrum/fftreal/TestSpeed.h b/demos/spectrum/fftreal/TestSpeed.h
new file mode 100644
index 0000000..2295781
--- /dev/null
+++ b/demos/spectrum/fftreal/TestSpeed.h
@@ -0,0 +1,95 @@
+/*****************************************************************************
+
+        TestSpeed.h
+        Copyright (c) 2005 Laurent de Soras
+
+--- Legal stuff ---
+
+This library is free software; you can redistribute it and/or
+modify it under the terms of the GNU Lesser General Public
+License as published by the Free Software Foundation; either
+version 2.1 of the License, or (at your option) any later version.
+
+This library is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+Lesser General Public License for more details.
+
+You should have received a copy of the GNU Lesser General Public
+License along with this library; if not, write to the Free Software
+Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
+
+*Tab=3***********************************************************************/
+
+
+
+#if ! defined (TestSpeed_HEADER_INCLUDED)
+#define	TestSpeed_HEADER_INCLUDED
+
+#if defined (_MSC_VER)
+	#pragma once
+	#pragma warning (4 : 4250) // "Inherits via dominance."
+#endif
+
+
+
+/*\\\ INCLUDE FILES \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+
+
+template <class FO>
+class TestSpeed
+{
+
+/*\\\ PUBLIC \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+public:
+
+	typedef	typename FO::DataType	DataType;
+
+   static int		perform_test_single_object (FO &fft);
+   static int		perform_test_d (FO &fft, const char *class_name_0);
+   static int		perform_test_i (FO &fft, const char *class_name_0);
+   static int		perform_test_di (FO &fft, const char *class_name_0);
+
+
+
+/*\\\ PROTECTED \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+protected:
+
+
+
+/*\\\ PRIVATE \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+private:
+
+	enum {			NBR_SPD_TESTS	= 10 * 1000 * 1000	};
+   enum {         MAX_NBR_TESTS  = 10000  };
+
+
+
+/*\\\ FORBIDDEN MEMBER FUNCTIONS \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+private:
+
+						TestSpeed ();
+						~TestSpeed ();
+						TestSpeed (const TestSpeed &other);
+	TestSpeed &		operator = (const TestSpeed &other);
+	bool				operator == (const TestSpeed &other);
+	bool				operator != (const TestSpeed &other);
+
+};	// class TestSpeed
+
+
+
+#include	"TestSpeed.hpp"
+
+
+
+#endif	// TestSpeed_HEADER_INCLUDED
+
+
+
+/*\\\ EOF \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
diff --git a/demos/spectrum/fftreal/TestSpeed.hpp b/demos/spectrum/fftreal/TestSpeed.hpp
new file mode 100644
index 0000000..e716b2a
--- /dev/null
+++ b/demos/spectrum/fftreal/TestSpeed.hpp
@@ -0,0 +1,223 @@
+/*****************************************************************************
+
+        TestSpeed.hpp
+        Copyright (c) 2005 Laurent de Soras
+
+--- Legal stuff ---
+
+This library is free software; you can redistribute it and/or
+modify it under the terms of the GNU Lesser General Public
+License as published by the Free Software Foundation; either
+version 2.1 of the License, or (at your option) any later version.
+
+This library is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+Lesser General Public License for more details.
+
+You should have received a copy of the GNU Lesser General Public
+License along with this library; if not, write to the Free Software
+Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
+
+*Tab=3***********************************************************************/
+
+
+
+#if defined (TestSpeed_CURRENT_CODEHEADER)
+	#error Recursive inclusion of TestSpeed code header.
+#endif
+#define	TestSpeed_CURRENT_CODEHEADER
+
+#if ! defined (TestSpeed_CODEHEADER_INCLUDED)
+#define	TestSpeed_CODEHEADER_INCLUDED
+
+
+
+/*\\\ INCLUDE FILES \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+#include	"test_fnc.h"
+#include	"stopwatch/StopWatch.h"
+#include	"TestWhiteNoiseGen.h"
+
+#include	<typeinfo>
+
+#include	<cstdio>
+
+
+
+/*\\\ PUBLIC \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+
+
+template <class FO>
+int	TestSpeed <FO>::perform_test_single_object (FO &fft)
+{
+	assert (&fft != 0);
+
+   int            ret_val = 0;
+
+	const std::type_info &	ti = typeid (fft);
+	const char *	class_name_0 = ti.name ();
+
+   if (ret_val == 0)
+   {
+	   perform_test_d (fft, class_name_0);
+   }
+   if (ret_val == 0)
+   {
+	   perform_test_i (fft, class_name_0);
+   }
+	if (ret_val == 0)
+   {
+      perform_test_di (fft, class_name_0);
+   }
+
+   if (ret_val == 0)
+   {
+      printf ("\n");
+   }
+
+   return (ret_val);
+}
+
+
+
+template <class FO>
+int	TestSpeed <FO>::perform_test_d (FO &fft, const char *class_name_0)
+{
+	assert (&fft != 0);
+   assert (class_name_0 != 0);
+
+	const long		len = fft.get_length ();
+   const long     nbr_tests = limit (
+      static_cast <long> (NBR_SPD_TESTS / len / len),
+      1L,
+      static_cast <long> (MAX_NBR_TESTS)
+   );
+
+	TestWhiteNoiseGen <DataType>	noise;
+	std::vector <DataType>	x (len, 0);
+	std::vector <DataType>	s (len);
+	noise.generate (&x [0], len);
+
+   printf (
+		"%s::do_fft () speed test [%ld samples]... ",
+		class_name_0,
+		len
+	);
+	fflush (stdout);
+
+	stopwatch::StopWatch	chrono;
+	chrono.start ();
+	for (long test = 0; test < nbr_tests; ++ test)
+	{
+		fft.do_fft (&s [0], &x [0]);
+		chrono.stop_lap ();
+	}
+
+	printf ("%.1f clocks/sample\n", chrono.get_time_best_lap (len));
+
+	return (0);
+}
+
+
+
+template <class FO>
+int	TestSpeed <FO>::perform_test_i (FO &fft, const char *class_name_0)
+{
+	assert (&fft != 0);
+   assert (class_name_0 != 0);
+
+	const long		len = fft.get_length ();
+   const long     nbr_tests = limit (
+      static_cast <long> (NBR_SPD_TESTS / len / len),
+      1L,
+      static_cast <long> (MAX_NBR_TESTS)
+   );
+
+	TestWhiteNoiseGen <DataType>	noise;
+	std::vector <DataType>	x (len);
+	std::vector <DataType>	s (len, 0);
+	noise.generate (&s [0], len);
+
+   printf (
+		"%s::do_ifft () speed test [%ld samples]... ",
+		class_name_0,
+		len
+	);
+	fflush (stdout);
+
+	stopwatch::StopWatch	chrono;
+	chrono.start ();
+	for (long test = 0; test < nbr_tests; ++ test)
+	{
+		fft.do_ifft (&s [0], &x [0]);
+		chrono.stop_lap ();
+	}
+
+	printf ("%.1f clocks/sample\n", chrono.get_time_best_lap (len));
+
+	return (0);
+}
+
+
+
+template <class FO>
+int	TestSpeed <FO>::perform_test_di (FO &fft, const char *class_name_0)
+{
+	assert (&fft != 0);
+   assert (class_name_0 != 0);
+
+	const long		len = fft.get_length ();
+   const long     nbr_tests = limit (
+      static_cast <long> (NBR_SPD_TESTS / len / len),
+      1L,
+      static_cast <long> (MAX_NBR_TESTS)
+   );
+
+	TestWhiteNoiseGen <DataType>	noise;
+	std::vector <DataType>	x (len, 0);
+	std::vector <DataType>	s (len);
+	std::vector <DataType>	y (len);
+	noise.generate (&x [0], len);
+
+   printf (
+		"%s::do_fft () / do_ifft () / rescale () speed test [%ld samples]... ",
+		class_name_0,
+		len
+	);
+	fflush (stdout);
+
+	stopwatch::StopWatch	chrono;
+
+	chrono.start ();
+	for (long test = 0; test < nbr_tests; ++ test)
+	{
+		fft.do_fft (&s [0], &x [0]);
+		fft.do_ifft (&s [0], &y [0]);
+		fft.rescale (&y [0]);
+		chrono.stop_lap ();
+	}
+
+	printf ("%.1f clocks/sample\n", chrono.get_time_best_lap (len));
+
+	return (0);
+}
+
+
+
+/*\\\ PROTECTED \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+
+
+/*\\\ PRIVATE \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+
+
+#endif	// TestSpeed_CODEHEADER_INCLUDED
+
+#undef TestSpeed_CURRENT_CODEHEADER
+
+
+
+/*\\\ EOF \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
diff --git a/demos/spectrum/fftreal/TestWhiteNoiseGen.h b/demos/spectrum/fftreal/TestWhiteNoiseGen.h
new file mode 100644
index 0000000..d815f8e
--- /dev/null
+++ b/demos/spectrum/fftreal/TestWhiteNoiseGen.h
@@ -0,0 +1,95 @@
+/*****************************************************************************
+
+        TestWhiteNoiseGen.h
+        Copyright (c) 2005 Laurent de Soras
+
+--- Legal stuff ---
+
+This library is free software; you can redistribute it and/or
+modify it under the terms of the GNU Lesser General Public
+License as published by the Free Software Foundation; either
+version 2.1 of the License, or (at your option) any later version.
+
+This library is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+Lesser General Public License for more details.
+
+You should have received a copy of the GNU Lesser General Public
+License along with this library; if not, write to the Free Software
+Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
+
+*Tab=3***********************************************************************/
+
+
+
+#if ! defined (TestWhiteNoiseGen_HEADER_INCLUDED)
+#define	TestWhiteNoiseGen_HEADER_INCLUDED
+
+#if defined (_MSC_VER)
+	#pragma once
+	#pragma warning (4 : 4250) // "Inherits via dominance."
+#endif
+
+
+
+/*\\\ INCLUDE FILES \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+
+
+template <class DT>
+class TestWhiteNoiseGen
+{
+
+/*\\\ PUBLIC \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+public:
+
+	typedef	DT	DataType;
+
+						TestWhiteNoiseGen ();
+	virtual			~TestWhiteNoiseGen () {}
+
+	void				generate (DataType data_ptr [], long len);
+
+
+
+/*\\\ PROTECTED \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+protected:
+
+
+
+/*\\\ PRIVATE \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+private:
+
+	typedef	unsigned long	StateType;
+
+	StateType		_rand_state;
+
+
+
+/*\\\ FORBIDDEN MEMBER FUNCTIONS \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+private:
+
+						TestWhiteNoiseGen (const TestWhiteNoiseGen &other);
+	TestWhiteNoiseGen &
+						operator = (const TestWhiteNoiseGen &other);
+	bool				operator == (const TestWhiteNoiseGen &other);
+	bool				operator != (const TestWhiteNoiseGen &other);
+
+};	// class TestWhiteNoiseGen
+
+
+
+#include	"TestWhiteNoiseGen.hpp"
+
+
+
+#endif	// TestWhiteNoiseGen_HEADER_INCLUDED
+
+
+
+/*\\\ EOF \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
diff --git a/demos/spectrum/fftreal/TestWhiteNoiseGen.hpp b/demos/spectrum/fftreal/TestWhiteNoiseGen.hpp
new file mode 100644
index 0000000..13b7eb3
--- /dev/null
+++ b/demos/spectrum/fftreal/TestWhiteNoiseGen.hpp
@@ -0,0 +1,91 @@
+/*****************************************************************************
+
+        TestWhiteNoiseGen.hpp
+        Copyright (c) 2005 Laurent de Soras
+
+--- Legal stuff ---
+
+This library is free software; you can redistribute it and/or
+modify it under the terms of the GNU Lesser General Public
+License as published by the Free Software Foundation; either
+version 2.1 of the License, or (at your option) any later version.
+
+This library is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+Lesser General Public License for more details.
+
+You should have received a copy of the GNU Lesser General Public
+License along with this library; if not, write to the Free Software
+Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
+
+*Tab=3***********************************************************************/
+
+
+
+#if defined (TestWhiteNoiseGen_CURRENT_CODEHEADER)
+	#error Recursive inclusion of TestWhiteNoiseGen code header.
+#endif
+#define	TestWhiteNoiseGen_CURRENT_CODEHEADER
+
+#if ! defined (TestWhiteNoiseGen_CODEHEADER_INCLUDED)
+#define	TestWhiteNoiseGen_CODEHEADER_INCLUDED
+
+
+
+/*\\\ INCLUDE FILES \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+
+
+/*\\\ PUBLIC \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+
+
+template <class DT>
+TestWhiteNoiseGen <DT>::TestWhiteNoiseGen ()
+:	_rand_state (0)
+{
+	_rand_state = reinterpret_cast <StateType> (this);
+}
+
+
+
+template <class DT>
+void	TestWhiteNoiseGen <DT>::generate (DataType data_ptr [], long len)
+{
+	assert (data_ptr != 0);
+	assert (len > 0);
+
+	const DataType	one = static_cast <DataType> (1);
+	const DataType	mul = one / static_cast <DataType> (0x80000000UL);
+
+	long				pos = 0;
+	do
+	{
+		const DataType	x = static_cast <DataType> (_rand_state & 0xFFFFFFFFUL);
+		data_ptr [pos] = x * mul - one;
+
+		_rand_state = _rand_state * 1234567UL + 890123UL;
+
+		++ pos;
+	}
+	while (pos < len);
+}
+
+
+
+/*\\\ PROTECTED \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+
+
+/*\\\ PRIVATE \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+
+
+#endif	// TestWhiteNoiseGen_CODEHEADER_INCLUDED
+
+#undef TestWhiteNoiseGen_CURRENT_CODEHEADER
+
+
+
+/*\\\ EOF \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
diff --git a/demos/spectrum/fftreal/bwins/fftrealu.def b/demos/spectrum/fftreal/bwins/fftrealu.def
new file mode 100644
index 0000000..7a79397
--- /dev/null
+++ b/demos/spectrum/fftreal/bwins/fftrealu.def
@@ -0,0 +1,5 @@
+EXPORTS
+	??0FFTRealWrapper@@QAE@XZ @ 1 NONAME ; FFTRealWrapper::FFTRealWrapper(void)
+	??1FFTRealWrapper@@QAE@XZ @ 2 NONAME ; FFTRealWrapper::~FFTRealWrapper(void)
+	?calculateFFT@FFTRealWrapper@@QAEXQAMQBM@Z @ 3 NONAME ; void FFTRealWrapper::calculateFFT(float * const, float const * const)
+
diff --git a/demos/spectrum/fftreal/def.h b/demos/spectrum/fftreal/def.h
new file mode 100644
index 0000000..99c545f
--- /dev/null
+++ b/demos/spectrum/fftreal/def.h
@@ -0,0 +1,60 @@
+/*****************************************************************************
+
+        def.h
+        Copyright (c) 2005 Laurent de Soras
+
+--- Legal stuff ---
+
+This library is free software; you can redistribute it and/or
+modify it under the terms of the GNU Lesser General Public
+License as published by the Free Software Foundation; either
+version 2.1 of the License, or (at your option) any later version.
+
+This library is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+Lesser General Public License for more details.
+
+You should have received a copy of the GNU Lesser General Public
+License along with this library; if not, write to the Free Software
+Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
+
+*Tab=3***********************************************************************/
+
+
+
+#if ! defined (def_HEADER_INCLUDED)
+#define	def_HEADER_INCLUDED
+
+#if defined (_MSC_VER)
+	#pragma once
+	#pragma warning (4 : 4250) // "Inherits via dominance."
+#endif
+
+
+
+/*\\\ INCLUDE FILES \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+
+
+
+const double	PI		= 3.1415926535897932384626433832795;
+const double	SQRT2	= 1.41421356237309514547462185873883;
+
+#if defined (_MSC_VER)
+
+	#define	FORCEINLINE	__forceinline
+
+#else
+
+	#define	FORCEINLINE	inline
+
+#endif
+
+
+
+#endif	// def_HEADER_INCLUDED
+
+
+
+/*\\\ EOF \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
diff --git a/demos/spectrum/fftreal/eabi/fftrealu.def b/demos/spectrum/fftreal/eabi/fftrealu.def
new file mode 100644
index 0000000..f95a441
--- /dev/null
+++ b/demos/spectrum/fftreal/eabi/fftrealu.def
@@ -0,0 +1,7 @@
+EXPORTS
+	_ZN14FFTRealWrapper12calculateFFTEPfPKf @ 1 NONAME
+	_ZN14FFTRealWrapperC1Ev @ 2 NONAME
+	_ZN14FFTRealWrapperC2Ev @ 3 NONAME
+	_ZN14FFTRealWrapperD1Ev @ 4 NONAME
+	_ZN14FFTRealWrapperD2Ev @ 5 NONAME
+
diff --git a/demos/spectrum/fftreal/fftreal.pas b/demos/spectrum/fftreal/fftreal.pas
new file mode 100644
index 0000000..ea63754
--- /dev/null
+++ b/demos/spectrum/fftreal/fftreal.pas
@@ -0,0 +1,661 @@
+(*****************************************************************************
+
+        DIGITAL SIGNAL PROCESSING TOOLS
+        Version 1.03, 2001/06/15
+        (c) 1999 - Laurent de Soras
+
+        FFTReal.h
+        Fourier transformation of real number arrays.
+        Portable ISO C++
+
+------------------------------------------------------------------------------
+
+	LEGAL
+
+	Source code may be freely used for any purpose, including commercial
+	applications. Programs must display in their "About" dialog-box (or
+	documentation) a text telling they use these routines by Laurent de Soras.
+	Modified source code can be distributed, but modifications must be clearly
+	indicated.
+
+	CONTACT
+
+	Laurent de Soras
+	92 avenue Albert 1er
+	92500 Rueil-Malmaison
+	France
+
+	ldesoras@club-internet.fr
+
+------------------------------------------------------------------------------
+
+        Translation to ObjectPascal by :
+          Frederic Vanmol
+          frederic@axiworld.be
+
+*****************************************************************************)
+
+
+unit
+    FFTReal;
+
+interface
+
+uses
+    Windows;
+
+(* Change this typedef to use a different floating point type in your FFTs
+	(i.e. float, double or long double). *)
+type
+    pflt_t = ^flt_t;
+    flt_t = single;
+
+    pflt_array = ^flt_array;
+    flt_array = array[0..0] of flt_t;
+
+    plongarray = ^longarray;
+    longarray = array[0..0] of longint;
+
+const
+     sizeof_flt : longint = SizeOf(flt_t);
+
+
+
+type
+    // Bit reversed look-up table nested class
+    TBitReversedLUT = class
+    private
+      _ptr : plongint;
+    public
+      constructor Create(const nbr_bits: integer);
+      destructor Destroy; override;
+      function get_ptr: plongint;
+    end;
+
+    // Trigonometric look-up table nested class
+    TTrigoLUT = class
+    private
+      _ptr : pflt_t;
+    public
+      constructor Create(const nbr_bits: integer);
+      destructor Destroy; override;
+      function get_ptr(const level: integer): pflt_t;
+    end;
+
+    TFFTReal = class
+    private
+      _bit_rev_lut  : TBitReversedLUT;
+      _trigo_lut    : TTrigoLUT;
+      _sqrt2_2      : flt_t;
+      _length       : longint;
+      _nbr_bits     : integer;
+      _buffer_ptr   : pflt_t;
+    public
+      constructor Create(const length: longint);
+      destructor Destroy; override;
+
+      procedure do_fft(f: pflt_array; const x: pflt_array);
+      procedure do_ifft(const f: pflt_array; x: pflt_array);
+      procedure rescale(x: pflt_array);
+    end;
+
+
+
+
+
+
+
+implementation
+
+uses
+    Math;
+
+{ TBitReversedLUT }
+
+constructor TBitReversedLUT.Create(const nbr_bits: integer);
+var
+   length   : longint;
+   cnt      : longint;
+   br_index : longint;
+   bit      : longint;
+begin
+  inherited Create;
+
+  length := 1 shl nbr_bits;
+  GetMem(_ptr, length*SizeOf(longint));
+
+  br_index := 0;
+  plongarray(_ptr)^[0] := 0;
+  for cnt := 1 to length-1 do
+  begin
+    // ++br_index (bit reversed)
+    bit := length shr 1;
+    br_index := br_index xor bit;
+    while br_index and bit = 0 do
+    begin
+      bit := bit shr 1;
+      br_index := br_index xor bit;
+    end;
+
+    plongarray(_ptr)^[cnt] := br_index;
+  end;
+end;
+
+destructor TBitReversedLUT.Destroy;
+begin
+  FreeMem(_ptr);
+  _ptr := nil;
+  inherited;
+end;
+
+function TBitReversedLUT.get_ptr: plongint;
+begin
+  Result := _ptr;
+end;
+
+{ TTrigLUT }
+
+constructor TTrigoLUT.Create(const nbr_bits: integer);
+var
+   total_len : longint;
+   PI        : double;
+   level     : integer;
+   level_len : longint;
+   level_ptr : pflt_array;
+   mul       : double;
+   i         : longint;
+begin
+  inherited Create;
+
+  _ptr := nil;
+
+  if (nbr_bits > 3) then
+  begin
+    total_len := (1 shl (nbr_bits - 1)) - 4;
+    GetMem(_ptr, total_len * sizeof_flt);
+
+    PI := ArcTan(1) * 4;
+    for level := 3 to nbr_bits-1 do
+    begin
+      level_len := 1 shl (level - 1);
+      level_ptr := pointer(get_ptr(level));
+      mul := PI / (level_len shl 1);
+
+      for i := 0 to level_len-1 do
+        level_ptr^[i] := cos(i * mul);
+    end;
+  end;
+end;
+
+destructor TTrigoLUT.Destroy;
+begin
+  FreeMem(_ptr);
+  _ptr := nil;
+  inherited;
+end;
+
+function TTrigoLUT.get_ptr(const level: integer): pflt_t;
+var
+   tempp : pflt_t;
+begin
+  tempp := _ptr;
+  inc(tempp, (1 shl (level-1)) - 4);
+  Result := tempp;
+end;
+
+{ TFFTReal }
+
+constructor TFFTReal.Create(const length: longint);
+begin
+  inherited Create;
+
+  _length := length;
+  _nbr_bits := Floor(Ln(length) / Ln(2) + 0.5);
+  _bit_rev_lut := TBitReversedLUT.Create(Floor(Ln(length) / Ln(2) + 0.5));
+  _trigo_lut := TTrigoLUT.Create(Floor(Ln(length) / Ln(2) + 0.05));
+  _sqrt2_2 := Sqrt(2) * 0.5;
+
+  _buffer_ptr := nil;
+  if _nbr_bits > 2 then
+    GetMem(_buffer_ptr, _length * sizeof_flt);
+end;
+
+destructor TFFTReal.Destroy;
+begin
+  if _buffer_ptr <> nil then
+  begin
+    FreeMem(_buffer_ptr);
+    _buffer_ptr := nil;
+  end;
+
+  _bit_rev_lut.Free;
+  _bit_rev_lut := nil;
+  _trigo_lut.Free;
+  _trigo_lut := nil;
+
+  inherited;       
+end;
+
+(*==========================================================================*/
+/*      Name: do_fft                                                        */
+/*      Description: Compute the FFT of the array.                          */
+/*      Input parameters:                                                   */
+/*        - x: pointer on the source array (time).                          */
+/*      Output parameters:                                                  */
+/*        - f: pointer on the destination array (frequencies).              */
+/*             f [0...length(x)/2] = real values,                           */
+/*             f [length(x)/2+1...length(x)-1] = imaginary values of        */
+/*               coefficents 1...length(x)/2-1.                             */
+/*==========================================================================*)
+procedure TFFTReal.do_fft(f: pflt_array; const x: pflt_array);
+var
+   sf, df     : pflt_array;
+   pass       : integer;
+   nbr_coef   : longint;
+   h_nbr_coef : longint;
+   d_nbr_coef : longint;
+   coef_index : longint;
+   bit_rev_lut_ptr : plongarray;
+   rev_index_0 : longint;
+   rev_index_1 : longint;
+   rev_index_2 : longint;
+   rev_index_3 : longint;
+   df2         : pflt_array;
+   n1, n2, n3  : integer;
+   sf_0, sf_2  : flt_t;
+   sqrt2_2     : flt_t;
+   v           : flt_t;
+   cos_ptr     : pflt_array;
+   i           : longint;
+   sf1r, sf2r  : pflt_array;
+   dfr, dfi    : pflt_array;
+   sf1i, sf2i  : pflt_array;
+   c, s        : flt_t;
+   temp_ptr    : pflt_array;
+   b_0, b_2    : flt_t;
+begin
+  n1 := 1;
+  n2 := 2;
+  n3 := 3;
+
+  (*______________________________________________
+   *
+   * General case
+   *______________________________________________
+   *)
+
+  if _nbr_bits > 2 then
+  begin
+    if _nbr_bits and 1 <> 0 then
+    begin
+      df := pointer(_buffer_ptr);
+      sf := f;
+    end
+    else
+    begin
+      df := f;
+      sf := pointer(_buffer_ptr);
+    end;
+
+    //
+    // Do the transformation in several passes
+    //
+
+    // First and second pass at once
+    bit_rev_lut_ptr := pointer(_bit_rev_lut.get_ptr);
+    coef_index := 0;
+
+    repeat
+      rev_index_0 := bit_rev_lut_ptr^[coef_index];
+      rev_index_1 := bit_rev_lut_ptr^[coef_index + 1];
+      rev_index_2 := bit_rev_lut_ptr^[coef_index + 2];
+      rev_index_3 := bit_rev_lut_ptr^[coef_index + 3];
+
+      df2 := pointer(longint(df) + (coef_index*sizeof_flt));
+      df2^[n1] := x^[rev_index_0] - x^[rev_index_1];
+      df2^[n3] := x^[rev_index_2] - x^[rev_index_3];
+
+      sf_0 := x^[rev_index_0] + x^[rev_index_1];
+      sf_2 := x^[rev_index_2] + x^[rev_index_3];
+
+      df2^[0] := sf_0 + sf_2;
+      df2^[n2] := sf_0 - sf_2;
+
+      inc(coef_index, 4);
+    until (coef_index >= _length);
+
+
+    // Third pass
+    coef_index := 0;
+    sqrt2_2 := _sqrt2_2;
+
+    repeat
+      sf^[coef_index] := df^[coef_index] + df^[coef_index + 4];
+      sf^[coef_index + 4] := df^[coef_index] - df^[coef_index + 4];
+      sf^[coef_index + 2] := df^[coef_index + 2];
+      sf^[coef_index + 6] := df^[coef_index + 6];
+
+      v := (df [coef_index + 5] - df^[coef_index + 7]) * sqrt2_2;
+      sf^[coef_index + 1] := df^[coef_index + 1] + v;
+      sf^[coef_index + 3] := df^[coef_index + 1] - v;
+
+      v := (df^[coef_index + 5] + df^[coef_index + 7]) * sqrt2_2;
+      sf [coef_index + 5] := v + df^[coef_index + 3];
+      sf [coef_index + 7] := v - df^[coef_index + 3];
+
+      inc(coef_index, 8);
+    until (coef_index >= _length);
+
+
+    // Next pass
+    for pass := 3 to _nbr_bits-1 do
+    begin
+      coef_index := 0;
+      nbr_coef := 1 shl pass;
+      h_nbr_coef := nbr_coef shr 1;
+      d_nbr_coef := nbr_coef shl 1;
+
+      cos_ptr := pointer(_trigo_lut.get_ptr(pass));
+      repeat
+        sf1r := pointer(longint(sf) + (coef_index * sizeof_flt));
+        sf2r := pointer(longint(sf1r) + (nbr_coef * sizeof_flt));
+        dfr := pointer(longint(df) + (coef_index * sizeof_flt));
+        dfi := pointer(longint(dfr) + (nbr_coef * sizeof_flt));
+
+        // Extreme coefficients are always real
+        dfr^[0] := sf1r^[0] + sf2r^[0];
+        dfi^[0] := sf1r^[0] - sf2r^[0];   // dfr [nbr_coef] =
+        dfr^[h_nbr_coef] := sf1r^[h_nbr_coef];
+        dfi^[h_nbr_coef] := sf2r^[h_nbr_coef];
+
+        // Others are conjugate complex numbers
+        sf1i := pointer(longint(sf1r) + (h_nbr_coef * sizeof_flt));
+        sf2i := pointer(longint(sf1i) + (nbr_coef * sizeof_flt));
+
+        for i := 1 to h_nbr_coef-1 do
+        begin
+          c := cos_ptr^[i];               // cos (i*PI/nbr_coef);
+          s := cos_ptr^[h_nbr_coef - i];  // sin (i*PI/nbr_coef);
+
+          v := sf2r^[i] * c - sf2i^[i] * s;
+          dfr^[i] := sf1r^[i] + v;
+          dfi^[-i] := sf1r^[i] - v;	// dfr [nbr_coef - i] =
+
+          v := sf2r^[i] * s + sf2i^[i] * c;
+          dfi^[i] := v + sf1i^[i];
+          dfi^[nbr_coef - i] := v - sf1i^[i];
+        end;
+
+        inc(coef_index, d_nbr_coef);
+      until (coef_index >= _length);
+
+      // Prepare to the next pass
+      temp_ptr := df;
+      df := sf;
+      sf := temp_ptr;
+    end;
+  end
+
+  (*______________________________________________
+   *
+   * Special cases
+   *______________________________________________
+   *)
+
+  // 4-point FFT
+  else if _nbr_bits = 2 then
+  begin
+    f^[n1] := x^[0] - x^[n2];
+    f^[n3] := x^[n1] - x^[n3];
+
+    b_0 := x^[0] + x^[n2];
+    b_2 := x^[n1] + x^[n3];
+
+    f^[0] := b_0 + b_2;
+    f^[n2] := b_0 - b_2;
+  end
+
+  // 2-point FFT
+  else if _nbr_bits = 1 then
+  begin
+    f^[0] := x^[0] + x^[n1];
+    f^[n1] := x^[0] - x^[n1];
+  end
+
+  // 1-point FFT
+  else
+    f^[0] := x^[0];
+end;
+
+
+(*==========================================================================*/
+/*      Name: do_ifft                                                       */
+/*      Description: Compute the inverse FFT of the array. Notice that      */
+/*                   IFFT (FFT (x)) = x * length (x). Data must be          */
+/*                   post-scaled.                                           */
+/*      Input parameters:                                                   */
+/*        - f: pointer on the source array (frequencies).                   */
+/*             f [0...length(x)/2] = real values,                           */
+/*             f [length(x)/2+1...length(x)-1] = imaginary values of        */
+/*               coefficents 1...length(x)/2-1.                             */
+/*      Output parameters:                                                  */
+/*        - x: pointer on the destination array (time).                     */
+/*==========================================================================*)
+procedure TFFTReal.do_ifft(const f: pflt_array; x: pflt_array);
+var
+   n1, n2, n3      : integer;
+   n4, n5, n6, n7  : integer;
+   sf, df, df_temp : pflt_array;
+   pass            : integer;
+   nbr_coef        : longint;
+   h_nbr_coef      : longint;
+   d_nbr_coef      : longint;
+   coef_index      : longint;
+   cos_ptr         : pflt_array;
+   i               : longint;
+   sfr, sfi        : pflt_array;
+   df1r, df2r      : pflt_array;
+   df1i, df2i      : pflt_array;
+   c, s, vr, vi    : flt_t;
+   temp_ptr        : pflt_array;
+   sqrt2_2         : flt_t;
+   bit_rev_lut_ptr : plongarray;
+   sf2             : pflt_array;
+   b_0, b_1, b_2, b_3 : flt_t;
+begin
+  n1 := 1;
+  n2 := 2;
+  n3 := 3;
+  n4 := 4;
+  n5 := 5;
+  n6 := 6;
+  n7 := 7;
+
+  (*______________________________________________
+   *
+   * General case
+   *______________________________________________
+   *)
+
+  if _nbr_bits > 2 then
+  begin
+    sf := f;
+
+    if _nbr_bits and 1 <> 0 then
+    begin
+      df := pointer(_buffer_ptr);
+      df_temp := x;
+    end
+    else
+    begin
+      df := x;
+      df_temp := pointer(_buffer_ptr);
+    end;
+
+    // Do the transformation in several pass
+
+    // First pass
+    for pass := _nbr_bits-1 downto 3 do
+    begin
+      coef_index := 0;
+      nbr_coef := 1 shl pass;
+      h_nbr_coef := nbr_coef shr 1;
+      d_nbr_coef := nbr_coef shl 1;
+
+      cos_ptr := pointer(_trigo_lut.get_ptr(pass));
+
+      repeat
+        sfr := pointer(longint(sf) + (coef_index*sizeof_flt));
+        sfi := pointer(longint(sfr) + (nbr_coef*sizeof_flt));
+        df1r := pointer(longint(df) + (coef_index*sizeof_flt));
+        df2r := pointer(longint(df1r) + (nbr_coef*sizeof_flt));
+
+        // Extreme coefficients are always real
+        df1r^[0] := sfr^[0] + sfi^[0];		// + sfr [nbr_coef]
+        df2r^[0] := sfr^[0] - sfi^[0];		// - sfr [nbr_coef]
+        df1r^[h_nbr_coef] := sfr^[h_nbr_coef] * 2;
+        df2r^[h_nbr_coef] := sfi^[h_nbr_coef] * 2;
+
+        // Others are conjugate complex numbers
+        df1i := pointer(longint(df1r) + (h_nbr_coef*sizeof_flt));
+        df2i := pointer(longint(df1i) + (nbr_coef*sizeof_flt));
+
+        for i := 1 to h_nbr_coef-1 do
+        begin
+          df1r^[i] := sfr^[i] + sfi^[-i];		// + sfr [nbr_coef - i]
+          df1i^[i] := sfi^[i] - sfi^[nbr_coef - i];
+
+          c := cos_ptr^[i];					// cos (i*PI/nbr_coef);
+          s := cos_ptr^[h_nbr_coef - i];	// sin (i*PI/nbr_coef);
+          vr := sfr^[i] - sfi^[-i];		// - sfr [nbr_coef - i]
+          vi := sfi^[i] + sfi^[nbr_coef - i];
+
+          df2r^[i] := vr * c + vi * s;
+          df2i^[i] := vi * c - vr * s;
+        end;
+
+        inc(coef_index, d_nbr_coef);
+      until (coef_index >= _length);
+
+
+      // Prepare to the next pass 
+      if (pass < _nbr_bits - 1) then
+      begin
+        temp_ptr := df;
+        df := sf;
+        sf := temp_ptr;
+      end
+      else
+      begin
+        sf := df;
+        df := df_temp;
+      end
+    end;
+
+    // Antepenultimate pass
+    sqrt2_2 := _sqrt2_2;
+    coef_index := 0;
+
+    repeat
+      df^[coef_index] := sf^[coef_index] + sf^[coef_index + 4];
+      df^[coef_index + 4] := sf^[coef_index] - sf^[coef_index + 4];
+      df^[coef_index + 2] := sf^[coef_index + 2] * 2;
+      df^[coef_index + 6] := sf^[coef_index + 6] * 2;
+
+      df^[coef_index + 1] := sf^[coef_index + 1] + sf^[coef_index + 3];
+      df^[coef_index + 3] := sf^[coef_index + 5] - sf^[coef_index + 7];
+
+      vr := sf^[coef_index + 1] - sf^[coef_index + 3];
+      vi := sf^[coef_index + 5] + sf^[coef_index + 7];
+
+      df^[coef_index + 5] := (vr + vi) * sqrt2_2;
+      df^[coef_index + 7] := (vi - vr) * sqrt2_2;
+
+      inc(coef_index, 8);
+    until (coef_index >= _length);
+
+
+    // Penultimate and last pass at once 
+    coef_index := 0;
+    bit_rev_lut_ptr := pointer(_bit_rev_lut.get_ptr);
+    sf2 := df;
+
+    repeat
+      b_0 := sf2^[0] + sf2^[n2];
+      b_2 := sf2^[0] - sf2^[n2];
+      b_1 := sf2^[n1] * 2;
+      b_3 := sf2^[n3] * 2;
+
+      x^[bit_rev_lut_ptr^[0]] := b_0 + b_1;
+      x^[bit_rev_lut_ptr^[n1]] := b_0 - b_1;
+      x^[bit_rev_lut_ptr^[n2]] := b_2 + b_3;
+      x^[bit_rev_lut_ptr^[n3]] := b_2 - b_3;
+
+      b_0 := sf2^[n4] + sf2^[n6];
+      b_2 := sf2^[n4] - sf2^[n6];
+      b_1 := sf2^[n5] * 2;
+      b_3 := sf2^[n7] * 2;
+
+      x^[bit_rev_lut_ptr^[n4]] := b_0 + b_1;
+      x^[bit_rev_lut_ptr^[n5]] := b_0 - b_1;
+      x^[bit_rev_lut_ptr^[n6]] := b_2 + b_3;
+      x^[bit_rev_lut_ptr^[n7]] := b_2 - b_3;
+
+      inc(sf2, 8);
+      inc(coef_index, 8);
+      inc(bit_rev_lut_ptr, 8);
+    until (coef_index >= _length);
+  end
+
+  (*______________________________________________
+   *
+   * Special cases
+   *______________________________________________
+   *)
+
+  // 4-point IFFT
+  else if _nbr_bits = 2 then
+  begin
+    b_0 := f^[0] + f [n2];
+    b_2 := f^[0] - f [n2];
+
+    x^[0] := b_0 + f [n1] * 2;
+    x^[n2] := b_0 - f [n1] * 2;
+    x^[n1] := b_2 + f [n3] * 2;
+    x^[n3] := b_2 - f [n3] * 2;
+  end
+
+  // 2-point IFFT
+  else if _nbr_bits = 1 then
+  begin
+    x^[0] := f^[0] + f^[n1];
+    x^[n1] := f^[0] - f^[n1];
+  end
+
+  // 1-point IFFT
+  else
+    x^[0] := f^[0];
+end;
+
+(*==========================================================================*/
+/*      Name: rescale                                                       */
+/*      Description: Scale an array by divide each element by its length.   */
+/*                   This function should be called after FFT + IFFT.       */
+/*      Input/Output parameters:                                            */
+/*        - x: pointer on array to rescale (time or frequency).             */
+/*==========================================================================*)
+procedure TFFTReal.rescale(x: pflt_array);
+var
+   mul  : flt_t;
+   i    : longint;
+begin
+  mul := 1.0 / _length;
+  i := _length - 1;
+
+  repeat
+    x^[i] := x^[i] * mul;
+    dec(i);
+  until (i < 0);
+end;
+
+end.
diff --git a/demos/spectrum/fftreal/fftreal.pro b/demos/spectrum/fftreal/fftreal.pro
new file mode 100644
index 0000000..786a962
--- /dev/null
+++ b/demos/spectrum/fftreal/fftreal.pro
@@ -0,0 +1,41 @@
+TEMPLATE = lib
+TARGET   = fftreal
+
+# FFTReal
+HEADERS  += Array.h \
+            Array.hpp \
+            DynArray.h \
+            DynArray.hpp \
+            FFTRealFixLen.h \
+            FFTRealFixLen.hpp \
+            FFTRealFixLenParam.h \
+            FFTRealPassDirect.h \
+            FFTRealPassDirect.hpp \
+            FFTRealPassInverse.h \
+            FFTRealPassInverse.hpp \
+            FFTRealSelect.h \
+            FFTRealSelect.hpp \
+            FFTRealUseTrigo.h \
+            FFTRealUseTrigo.hpp \
+            OscSinCos.h \
+            OscSinCos.hpp \
+            def.h
+	    
+# Wrapper used to export the required instantiation of the FFTRealFixLen template
+HEADERS  += fftreal_wrapper.h
+SOURCES  += fftreal_wrapper.cpp
+
+DEFINES  += FFTREAL_LIBRARY
+
+symbian {
+    # Provide unique ID for the generated binary, required by Symbian OS
+    TARGET.UID3 = 0xA000E3FB
+} else {
+    macx {
+        CONFIG += lib_bundle
+    } else {
+        DESTDIR = ../bin
+    }
+} 
+
+
diff --git a/demos/spectrum/fftreal/fftreal_wrapper.cpp b/demos/spectrum/fftreal/fftreal_wrapper.cpp
new file mode 100644
index 0000000..50ab36d
--- /dev/null
+++ b/demos/spectrum/fftreal/fftreal_wrapper.cpp
@@ -0,0 +1,54 @@
+/***************************************************************************
+**
+** Copyright (C) 2010 Nokia Corporation and/or its subsidiary(-ies).
+** Contact: Nokia Corporation (qt-info@nokia.com)
+**
+** This file is part of the examples of the Qt Toolkit.
+**
+** This program is free software: you can redistribute it and/or modify
+** it under the terms of the GNU Lesser General Public License as
+** published by the Free Software Foundation, either version 2.1. This
+** program is distributed in the hope that it will be useful, but WITHOUT
+** ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
+** FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
+** for more details. You should have received a copy of the GNU General
+** Public License along with this program. If not, see
+** <http://www.gnu.org/licenses/>.
+**
+***************************************************************************/
+
+#include "fftreal_wrapper.h"
+
+// FFTReal code generates quite a lot of 'unused parameter' compiler warnings,
+// which we suppress here in order to get a clean build output.
+#if defined Q_CC_MSVC
+#    pragma warning(disable:4100)
+#elif defined Q_CC_GNU
+#    pragma GCC diagnostic ignored "-Wunused-parameter"
+#elif defined Q_CC_MWERKS
+#    pragma warning off (10182)
+#endif
+
+#include "FFTRealFixLen.h"
+
+class FFTRealWrapperPrivate {
+public:
+    FFTRealFixLen<FFTLengthPowerOfTwo> m_fft;
+};
+
+
+FFTRealWrapper::FFTRealWrapper()
+    :   m_private(new FFTRealWrapperPrivate)
+{
+
+}
+
+FFTRealWrapper::~FFTRealWrapper()
+{
+    delete m_private;
+}
+
+void FFTRealWrapper::calculateFFT(DataType in[], const DataType out[])
+{
+    m_private->m_fft.do_fft(in, out);
+}
diff --git a/demos/spectrum/fftreal/fftreal_wrapper.h b/demos/spectrum/fftreal/fftreal_wrapper.h
new file mode 100644
index 0000000..48d614e
--- /dev/null
+++ b/demos/spectrum/fftreal/fftreal_wrapper.h
@@ -0,0 +1,63 @@
+/***************************************************************************
+**
+** Copyright (C) 2010 Nokia Corporation and/or its subsidiary(-ies).
+** Contact: Nokia Corporation (qt-info@nokia.com)
+**
+** This file is part of the examples of the Qt Toolkit.
+**
+** This program is free software: you can redistribute it and/or modify
+** it under the terms of the GNU Lesser General Public License as
+** published by the Free Software Foundation, either version 2.1. This
+** program is distributed in the hope that it will be useful, but WITHOUT
+** ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
+** FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
+** for more details. You should have received a copy of the GNU General
+** Public License along with this program. If not, see
+** <http://www.gnu.org/licenses/>.
+**
+***************************************************************************/
+
+#ifndef FFTREAL_WRAPPER_H
+#define FFTREAL_WRAPPER_H
+
+#include <QtCore/QtGlobal>
+
+#if defined(FFTREAL_LIBRARY)
+#  define FFTREAL_EXPORT Q_DECL_EXPORT
+#else
+#  define FFTREAL_EXPORT Q_DECL_IMPORT
+#endif
+
+class FFTRealWrapperPrivate;
+
+// Each pass of the FFT processes 2^X samples, where X is the
+// number below.
+static const int FFTLengthPowerOfTwo = 12;
+
+/**
+ * Wrapper around the FFTRealFixLen template provided by the FFTReal
+ * library
+ *
+ * This class instantiates a single instance of FFTRealFixLen, using
+ * FFTLengthPowerOfTwo as the template parameter.  It then exposes
+ * FFTRealFixLen<FFTLengthPowerOfTwo>::do_fft via the calculateFFT
+ * function, thereby allowing an application to dynamically link
+ * against the FFTReal implementation.
+ *
+ * See http://ldesoras.free.fr/prod.html
+ */
+class FFTREAL_EXPORT FFTRealWrapper
+{
+public:
+    FFTRealWrapper();
+    ~FFTRealWrapper();
+
+    typedef float DataType;
+    void calculateFFT(DataType in[], const DataType out[]);
+
+private:
+    FFTRealWrapperPrivate*  m_private;
+};
+
+#endif // FFTREAL_WRAPPER_H
+
diff --git a/demos/spectrum/fftreal/license.txt b/demos/spectrum/fftreal/license.txt
new file mode 100644
index 0000000..918fe68
--- /dev/null
+++ b/demos/spectrum/fftreal/license.txt
@@ -0,0 +1,459 @@
+		  GNU LESSER GENERAL PUBLIC LICENSE
+		       Version 2.1, February 1999
+
+ Copyright (C) 1991, 1999 Free Software Foundation, Inc.
+     59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
+ Everyone is permitted to copy and distribute verbatim copies
+ of this license document, but changing it is not allowed.
+
+[This is the first released version of the Lesser GPL.  It also counts
+ as the successor of the GNU Library Public License, version 2, hence
+ the version number 2.1.]
+
+			    Preamble
+
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diff --git a/demos/spectrum/fftreal/readme.txt b/demos/spectrum/fftreal/readme.txt
new file mode 100644
index 0000000..0c5ce16
--- /dev/null
+++ b/demos/spectrum/fftreal/readme.txt
@@ -0,0 +1,242 @@
+==============================================================================
+
+        FFTReal
+        Version 2.00, 2005/10/18
+
+        Fourier transformation (FFT, IFFT) library specialised for real data
+        Portable ISO C++
+
+        (c) Laurent de Soras <laurent.de.soras@club-internet.fr>
+        Object Pascal port (c) Frederic Vanmol <frederic@fruityloops.com>
+
+==============================================================================
+
+
+
+1. Legal
+--------
+
+This library is free software; you can redistribute it and/or
+modify it under the terms of the GNU Lesser General Public
+License as published by the Free Software Foundation; either
+version 2.1 of the License, or (at your option) any later version.
+
+This library is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+Lesser General Public License for more details.
+
+You should have received a copy of the GNU Lesser General Public
+License along with this library; if not, write to the Free Software
+Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
+
+Check the file license.txt to get full information about the license.
+
+
+
+2. Content
+----------
+
+FFTReal is a library to compute Discrete Fourier Transforms (DFT) with the
+FFT algorithm (Fast Fourier Transform) on arrays of real numbers. It can
+also compute the inverse transform.
+
+You should find in this package a lot of files ; some of them are of interest:
+- readme.txt: you are reading it
+- FFTReal.h: FFT, length fixed at run-time
+- FFTRealFixLen.h: FFT, length fixed at compile-time
+- FFTReal.pas: Pascal implementation (working but not up-to-date)
+- stopwatch directory
+
+
+
+3. Using FFTReal
+----------------
+
+Important - if you were using older versions of FFTReal (up to 1.03), some
+things have changed. FFTReal is now a template. Therefore use FFTReal<float>
+or FFTReal<double> in your code depending on the application datatype. The
+flt_t typedef has been removed.
+
+You have two ways to use FFTReal. In the first way, the FFT has its length
+fixed at run-time, when the object is instanciated. It means that you have
+not to know the length when you write the code. This is the usual way of
+proceeding.
+
+
+3.1 FFTReal - Length fixed at run-time
+--------------------------------------
+
+Just instanciate one time a FFTReal object. Specify the data type you want
+as template parameter (only floating point: float, double, long double or
+custom type). The constructor precompute a lot of things, so it may be a bit
+long. The parameter is the number of points used for the next FFTs. It must
+be a power of 2:
+
+   #include "FFTReal.h"
+   ...
+   long len = 1024;
+   ...
+   FFTReal <float> fft_object (len);   // 1024-point FFT object constructed.
+
+Then you can use this object to compute as many FFTs and IFFTs as you want.
+They will be computed very quickly because a lot of work has been done in the
+object construction.
+
+   float x [1024];
+   float f [1024];
+
+   ...
+   fft_object.do_fft (f, x);     // x (real) --FFT---> f (complex)
+   ...
+   fft_object.do_ifft (f, x);    // f (complex) --IFFT--> x (real)
+   fft_object.rescale (x);       // Post-scaling should be done after FFT+IFFT
+   ...
+
+x [] and f [] are floating point number arrays. x [] is the real number
+sequence which we want to compute the FFT. f [] is the result, in the
+"frequency" domain. f has the same number of elements as x [], but f []
+elements are complex numbers. The routine uses some FFT properties to
+optimize memory and to reduce calculations: the transformaton of a real
+number sequence is a conjugate complex number sequence: F [k] = F [-k]*.
+
+
+3.2 FFTRealFixLen - Length fixed at compile-time
+------------------------------------------------
+
+This class is significantly faster than the previous one, giving a speed
+gain between 50 and 100 %. The template parameter is the base-2 logarithm of
+the FFT length. The datatype is float; it can be changed by modifying the
+DataType typedef in FFTRealFixLenParam.h. As FFTReal class, it supports
+only floating-point types or equivalent.
+
+To instanciate the object, just proceed as below:
+
+   #include "FFTRealFixLen.h"
+   ...
+   FFTRealFixLen <10> fft_object; // 1024-point (2^10) FFT object constructed.
+
+Use is similar as the one of FFTReal.
+
+
+3.3 Data organisation
+---------------------
+
+Mathematically speaking, the formulas below show what does FFTReal:
+
+do_fft() : f(k) = sum (p = 0, N-1, x(p) * exp (+j*2*pi*k*p/N))
+do_ifft(): x(k) = sum (p = 0, N-1, f(p) * exp (-j*2*pi*k*p/N))
+
+Where j is the square root of -1. The formulas differ only by the sign of
+the exponential. When the sign is positive, the transform is called positive.
+Common formulas for Fourier transform are negative for the direct tranform and
+positive for the inverse one.
+
+However in these formulas, f is an array of complex numbers and doesn't
+correspound exactly to the f[] array taken as function parameter. The
+following table shows how the f[] sequence is mapped onto the usable FFT
+coefficients (called bins):
+
+   FFTReal output | Positive FFT equiv.   | Negative FFT equiv.
+   ---------------+-----------------------+-----------------------
+   f [0]          | Real (bin 0)          | Real (bin 0)
+   f [...]        | Real (bin ...)        | Real (bin ...)
+   f [length/2]   | Real (bin length/2)   | Real (bin length/2)
+   f [length/2+1] | Imag (bin 1)          | -Imag (bin 1)
+   f [...]        | Imag (bin ...)        | -Imag (bin ...)
+   f [length-1]   | Imag (bin length/2-1) | -Imag (bin length/2-1)
+
+And FFT bins are distributed in f [] as above:
+
+               |                | Positive FFT    | Negative FFT
+   Bin         | Real part      | imaginary part  | imaginary part
+   ------------+----------------+-----------------+---------------
+   0           | f [0]          | 0               | 0
+   1           | f [1]          | f [length/2+1]  | -f [length/2+1]
+   ...         | f [...],       | f [...]         | -f [...]
+   length/2-1  | f [length/2-1] | f [length-1]    | -f [length-1]
+   length/2    | f [length/2]   | 0               | 0
+   length/2+1  | f [length/2-1] | -f [length-1]   | f [length-1]
+   ...         | f [...]        | -f [...]        | f [...]
+   length-1    | f [1]          | -f [length/2+1] | f [length/2+1]
+
+f [] coefficients have the same layout for FFT and IFFT functions. You may
+notice that scaling must be done if you want to retrieve x after FFT and IFFT.
+Actually, IFFT (FFT (x)) = x * length(x). This is a not a problem because
+most of the applications don't care about absolute values. Thus, the operation
+requires less calculation. If you want to use the FFT and IFFT to transform a
+signal, you have to apply post- (or pre-) processing yourself. Multiplying
+or dividing floating point numbers by a power of 2 doesn't generate extra
+computation noise.
+
+
+
+4. Compilation and testing
+--------------------------
+
+Drop the following files into your project or makefile:
+
+Array.*
+def.h
+DynArray.*
+FFTReal*.cpp
+FFTReal*.h*
+OscSinCos.*
+
+Other files are for testing purpose only, do not include them if you just need
+to use the library ; they are not needed to use FFTReal in your own programs.
+
+FFTReal may be compiled in two versions: release and debug. Debug version
+has checks that could slow down the code. Define NDEBUG to set the Release
+mode. For example, the command line to compile the test bench on GCC would
+look like:
+
+Debug mode:
+g++ -Wall -o fftreal_debug.exe *.cpp stopwatch/*.cpp
+
+Release mode:
+g++ -Wall -o fftreal_release.exe -DNDEBUG -O3 *.cpp stopwatch/*.cpp
+
+It may be tricky to compile the test bench because the speed tests use the
+stopwatch sub-library, which is not that cross-platform. If you encounter
+any problem that you cannot easily fix while compiling it, edit the file
+test_settings.h and un-define the speed test macro. Remove the stopwatch
+directory from your source file list, too.
+
+If it's not done by default, you should activate the exception handling
+of your compiler to get the class memory-leak-safe. Thus, when a memory
+allocation fails (in the constructor), an exception is thrown and the entire
+object is safely destructed. It reduces the permanent error checking overhead
+in the client code. Also, the test bench requires Run-Time Type Information
+(RTTI) to be enabled in order to display the names of the tested classes -
+sometimes mangled, depending on the compiler.
+
+The test bench may take a long time to compile, especially in Release mode,
+because a lot of recursive templates are instanciated.
+
+
+
+5. History
+----------
+
+v2.00 (2005.10.18)
+- Turned FFTReal class into template (data type as parameter)
+- Added FFTRealFixLen
+- Trigonometric tables are size-limited in order to preserve cache memory;
+over a given size, sin/cos functions are computed on the fly.
+- Better test bench for accuracy and speed
+
+v1.03 (2001.06.15)
+- Thanks to Frederic Vanmol for the Pascal port (works with Delphi).
+- Documentation improvement
+
+v1.02 (2001.03.25)
+- sqrt() is now precomputed when the object FFTReal is constructed, resulting
+in speed impovement for small size FFT.
+
+v1.01 (2000)
+- Small modifications, I don't remember what.
+
+v1.00 (1999.08.14)
+- First version released
+
diff --git a/demos/spectrum/fftreal/stopwatch/ClockCycleCounter.cpp b/demos/spectrum/fftreal/stopwatch/ClockCycleCounter.cpp
new file mode 100644
index 0000000..fe1d424
--- /dev/null
+++ b/demos/spectrum/fftreal/stopwatch/ClockCycleCounter.cpp
@@ -0,0 +1,285 @@
+/*****************************************************************************
+
+        ClockCycleCounter.cpp
+        Copyright (c) 2003 Laurent de Soras
+
+--- Legal stuff ---
+
+This library is free software; you can redistribute it and/or
+modify it under the terms of the GNU Lesser General Public
+License as published by the Free Software Foundation; either
+version 2.1 of the License, or (at your option) any later version.
+
+This library is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+Lesser General Public License for more details.
+
+You should have received a copy of the GNU Lesser General Public
+License along with this library; if not, write to the Free Software
+Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
+
+*Tab=3***********************************************************************/
+
+
+
+#if defined (_MSC_VER)
+	#pragma warning (1 : 4130) // "'operator' : logical operation on address of string constant"
+	#pragma warning (1 : 4223) // "nonstandard extension used : non-lvalue array converted to pointer"
+	#pragma warning (1 : 4705) // "statement has no effect"
+	#pragma warning (1 : 4706) // "assignment within conditional expression"
+	#pragma warning (4 : 4786) // "identifier was truncated to '255' characters in the debug information"
+	#pragma warning (4 : 4800) // "forcing value to bool 'true' or 'false' (performance warning)"
+	#pragma warning (4 : 4355) // "'this' : used in base member initializer list"
+#endif
+
+
+
+/*\\\ INCLUDE FILES \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+#include	"ClockCycleCounter.h"
+
+#include	<cassert>
+
+
+
+namespace stopwatch
+{
+
+
+
+/*\\\ PUBLIC \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+
+
+/*
+==============================================================================
+Name: ctor
+Description:
+	The first object constructed initialise global data. This first
+	construction may be a bit slow.
+Throws: Nothing
+==============================================================================
+*/
+
+ClockCycleCounter::ClockCycleCounter ()
+:	_start_time (0)
+,	_state (0)
+,	_best_score (-1)
+{
+	if (! _init_flag)
+	{
+		// Should be executed in this order
+		compute_clk_mul ();
+		compute_measure_time_total ();
+		compute_measure_time_lap ();
+
+		// Restores object state
+		_start_time = 0;
+		_state      = 0;
+		_best_score = -1;
+
+		_init_flag = true;
+	}
+}
+
+
+
+/*
+==============================================================================
+Name: get_time_total
+Description:
+	Gives the time elapsed between the latest stop_lap() and start() calls.
+Returns:
+	The duration, in clock cycles.
+Throws: Nothing
+==============================================================================
+*/
+
+Int64	ClockCycleCounter::get_time_total () const
+{
+	const Int64		duration = _state - _start_time;
+	assert (duration >= 0);
+
+	const Int64		t = max (
+		duration - _measure_time_total,
+		static_cast <Int64> (0)
+	);
+
+	return (t * _clk_mul);
+}
+
+
+
+/*
+==============================================================================
+Name: get_time_best_lap
+Description:
+	Gives the smallest time between two consecutive stop_lap() or between
+	the stop_lap() and start(). The value is reset by a call to start().
+	Call this function only after a stop_lap().
+	The time is amputed from the duration of the stop_lap() call itself.
+Returns:
+	The smallest duration, in clock cycles.
+Throws: Nothing
+==============================================================================
+*/
+
+Int64	ClockCycleCounter::get_time_best_lap () const
+{
+	assert (_best_score >= 0);
+
+	const Int64		t1 = max (
+		_best_score - _measure_time_lap,
+		static_cast <Int64> (0)
+	);
+	const Int64		t = min (t1, get_time_total ());
+
+	return (t * _clk_mul);
+}
+
+
+
+/*\\\ PROTECTED \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+
+
+/*\\\ PRIVATE \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+
+
+#if defined (__MACOS__)
+
+static inline double	stopwatch_ClockCycleCounter_get_time_s ()
+{
+	const Nanoseconds	ns = AbsoluteToNanoseconds (UpTime ());
+
+	return (ns.hi * 4294967296e-9 + ns.lo * 1e-9);
+}
+
+#endif	// __MACOS__
+
+
+
+/*
+==============================================================================
+Name: compute_clk_mul
+Description:
+	This function, only for PowerPC/MacOS computers, computes the multiplier
+	required to deduce clock cycles from the internal counter.
+Throws: Nothing
+==============================================================================
+*/
+
+void	ClockCycleCounter::compute_clk_mul ()
+{
+	assert (! _init_flag);
+
+#if defined (__MACOS__)
+
+	long				clk_speed_mhz = CurrentProcessorSpeed ();
+	const Int64		clk_speed =
+		static_cast <Int64> (clk_speed_mhz) * (1000L*1000L);
+
+	const double	start_time_s = stopwatch_ClockCycleCounter_get_time_s ();
+	start ();
+
+	const double	duration = 0.01;	// Seconds
+	while (stopwatch_ClockCycleCounter_get_time_s () - start_time_s < duration)
+	{
+		continue;
+	}
+
+	const double	stop_time_s = stopwatch_ClockCycleCounter_get_time_s ();
+	stop ();
+
+	const double	diff_time_s = stop_time_s - start_time_s;
+	const double	nbr_cycles = diff_time_s * static_cast <double> (clk_speed);
+
+	const Int64		diff_time_c = _state - _start_time;
+	const double	clk_mul = nbr_cycles / static_cast <double> (diff_time_c);
+
+	_clk_mul = round_int (clk_mul);
+
+#endif	// __MACOS__
+}
+
+
+
+void	ClockCycleCounter::compute_measure_time_total ()
+{
+	start ();
+	spend_time ();
+
+	Int64				best_result = 0x7FFFFFFFL;	// Should be enough
+	long				nbr_tests = 100;
+	for (long cnt = 0; cnt < nbr_tests; ++cnt)
+	{
+		start ();
+		stop_lap ();
+		const Int64		duration = _state - _start_time;
+		best_result = min (best_result, duration);
+	}
+
+	_measure_time_total = best_result;
+}
+
+
+
+/*
+==============================================================================
+Name: compute_measure_time_lap
+Description:
+	Computes the duration of one stop_lap() call and store it. It will be used
+	later to get the real duration of the measured operation (by substracting
+	the measurement duration).
+Throws: Nothing
+==============================================================================
+*/
+
+void	ClockCycleCounter::compute_measure_time_lap ()
+{
+	start ();
+	spend_time ();
+
+	long				nbr_tests = 10;
+	for (long cnt = 0; cnt < nbr_tests; ++cnt)
+	{
+		stop_lap ();
+		stop_lap ();
+		stop_lap ();
+		stop_lap ();
+	}
+
+	_measure_time_lap = _best_score;
+}
+
+
+
+void	ClockCycleCounter::spend_time ()
+{
+	const Int64		nbr_clocks = 500;	// Number of clock cycles to spend
+
+	const Int64		start = read_clock_counter ();
+	Int64				current;
+
+	do
+	{
+		current = read_clock_counter ();
+	}
+	while ((current - start) * _clk_mul < nbr_clocks);
+}
+
+
+
+Int64	ClockCycleCounter::_measure_time_total = 0;
+Int64	ClockCycleCounter::_measure_time_lap = 0;
+int	ClockCycleCounter::_clk_mul = 1;
+bool	ClockCycleCounter::_init_flag = false;
+
+
+}	// namespace stopwatch
+
+
+
+/*\\\ EOF \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
diff --git a/demos/spectrum/fftreal/stopwatch/ClockCycleCounter.h b/demos/spectrum/fftreal/stopwatch/ClockCycleCounter.h
new file mode 100644
index 0000000..ba7a99a
--- /dev/null
+++ b/demos/spectrum/fftreal/stopwatch/ClockCycleCounter.h
@@ -0,0 +1,124 @@
+/*****************************************************************************
+
+        ClockCycleCounter.h
+        Copyright (c) 2003 Laurent de Soras
+
+Instrumentation class, for accurate time interval measurement. You may have
+to modify the implementation to adapt it to your system and/or compiler.
+
+--- Legal stuff ---
+
+This library is free software; you can redistribute it and/or
+modify it under the terms of the GNU Lesser General Public
+License as published by the Free Software Foundation; either
+version 2.1 of the License, or (at your option) any later version.
+
+This library is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+Lesser General Public License for more details.
+
+You should have received a copy of the GNU Lesser General Public
+License along with this library; if not, write to the Free Software
+Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
+
+*Tab=3***********************************************************************/
+
+
+
+#if ! defined (stopwatch_ClockCycleCounter_HEADER_INCLUDED)
+#define	stopwatch_ClockCycleCounter_HEADER_INCLUDED
+
+#if defined (_MSC_VER)
+	#pragma once
+	#pragma warning (4 : 4250) // "Inherits via dominance."
+#endif
+
+
+
+/*\\\ INCLUDE FILES \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+#include	"def.h"
+#include	"Int64.h"
+
+
+
+namespace stopwatch
+{
+
+
+
+class ClockCycleCounter
+{
+
+/*\\\ PUBLIC \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+public:
+
+						ClockCycleCounter ();
+
+	stopwatch_FORCEINLINE void
+						start ();
+	stopwatch_FORCEINLINE void
+						stop_lap ();
+	Int64				get_time_total () const;
+	Int64				get_time_best_lap () const;
+
+
+
+/*\\\ PROTECTED \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+protected:
+
+
+
+/*\\\ PRIVATE \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+private:
+
+	void				compute_clk_mul ();
+	void				compute_measure_time_total ();
+	void				compute_measure_time_lap ();
+
+	static void		spend_time ();
+	static stopwatch_FORCEINLINE Int64
+						read_clock_counter ();
+
+	Int64				_start_time;
+	Int64				_state;
+	Int64				_best_score;
+
+	static Int64	_measure_time_total;
+	static Int64	_measure_time_lap;
+	static int		_clk_mul;
+	static bool		_init_flag;
+
+
+
+/*\\\ FORBIDDEN MEMBER FUNCTIONS \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+private:
+
+						ClockCycleCounter (const ClockCycleCounter &other);
+	ClockCycleCounter &
+						operator = (const ClockCycleCounter &other);
+	bool				operator == (const ClockCycleCounter &other);
+	bool				operator != (const ClockCycleCounter &other);
+
+};	// class ClockCycleCounter
+
+
+
+}	// namespace stopwatch
+
+
+
+#include	"ClockCycleCounter.hpp"
+
+
+
+#endif	// stopwatch_ClockCycleCounter_HEADER_INCLUDED
+
+
+
+/*\\\ EOF \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
diff --git a/demos/spectrum/fftreal/stopwatch/ClockCycleCounter.hpp b/demos/spectrum/fftreal/stopwatch/ClockCycleCounter.hpp
new file mode 100644
index 0000000..fbd511e
--- /dev/null
+++ b/demos/spectrum/fftreal/stopwatch/ClockCycleCounter.hpp
@@ -0,0 +1,150 @@
+/*****************************************************************************
+
+        ClockCycleCounter.hpp
+        Copyright (c) 2003 Laurent de Soras
+
+Please complete the definitions according to your compiler/architecture.
+It's not a big deal if it's not possible to get the clock count...
+
+--- Legal stuff ---
+
+This library is free software; you can redistribute it and/or
+modify it under the terms of the GNU Lesser General Public
+License as published by the Free Software Foundation; either
+version 2.1 of the License, or (at your option) any later version.
+
+This library is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+Lesser General Public License for more details.
+
+You should have received a copy of the GNU Lesser General Public
+License along with this library; if not, write to the Free Software
+Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
+
+*Tab=3***********************************************************************/
+
+
+
+#if defined (stopwatch_ClockCycleCounter_CURRENT_CODEHEADER)
+	#error Recursive inclusion of ClockCycleCounter code header.
+#endif
+#define	stopwatch_ClockCycleCounter_CURRENT_CODEHEADER
+
+#if ! defined (stopwatch_ClockCycleCounter_CODEHEADER_INCLUDED)
+#define	stopwatch_ClockCycleCounter_CODEHEADER_INCLUDED
+
+
+
+/*\\\ INCLUDE FILES \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+#include	"fnc.h"
+
+#include	<climits>
+
+
+
+namespace stopwatch
+{
+
+
+
+/*\\\ PUBLIC \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+
+
+/*
+==============================================================================
+Name: start
+Description:
+	Starts the counter.
+Throws: Nothing
+==============================================================================
+*/
+
+void	ClockCycleCounter::start ()
+{
+	_best_score = (static_cast <Int64> (1) << (sizeof (Int64) * CHAR_BIT - 2));
+	const Int64		start_clock = read_clock_counter ();
+	_start_time = start_clock;
+	_state = start_clock - _best_score;
+}
+
+
+
+/*
+==============================================================================
+Name: stop_lap
+Description:
+	Captures the current time and updates the smallest duration between two
+	consecutive calls to stop_lap() or the latest start().
+	start() must have been called at least once before calling this function.
+Throws: Nothing
+==============================================================================
+*/
+
+void	ClockCycleCounter::stop_lap ()
+{
+	const Int64		end_clock = read_clock_counter ();
+	_best_score = min (end_clock - _state, _best_score);
+	_state = end_clock;
+}
+
+
+
+/*\\\ PROTECTED \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+
+
+/*\\\ PRIVATE \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+
+
+Int64	ClockCycleCounter::read_clock_counter ()
+{
+	register Int64		clock_cnt;
+
+#if defined (_MSC_VER)
+
+	__asm
+	{
+		lea				edi, clock_cnt
+		rdtsc
+		mov				[edi    ], eax
+		mov				[edi + 4], edx
+	}
+
+#elif defined (__GNUC__) && defined (__i386__)
+
+	__asm__ __volatile__ ("rdtsc" : "=A" (clock_cnt));
+
+#elif (__MWERKS__) && defined (__POWERPC__) 
+	
+	asm
+	{
+	loop:
+		mftbu			clock_cnt@hiword
+		mftb			clock_cnt@loword
+		mftbu			r5
+		cmpw			clock_cnt@hiword,r5
+		bne loop
+	}
+	
+#endif
+
+	return (clock_cnt);
+}
+
+
+
+}	// namespace stopwatch
+
+
+
+#endif	// stopwatch_ClockCycleCounter_CODEHEADER_INCLUDED
+
+#undef stopwatch_ClockCycleCounter_CURRENT_CODEHEADER
+
+
+
+/*\\\ EOF \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
diff --git a/demos/spectrum/fftreal/stopwatch/Int64.h b/demos/spectrum/fftreal/stopwatch/Int64.h
new file mode 100644
index 0000000..1e786e2
--- /dev/null
+++ b/demos/spectrum/fftreal/stopwatch/Int64.h
@@ -0,0 +1,71 @@
+/*****************************************************************************
+
+        Int64.h
+        Copyright (c) 2003 Laurent de Soras
+
+--- Legal stuff ---
+
+This library is free software; you can redistribute it and/or
+modify it under the terms of the GNU Lesser General Public
+License as published by the Free Software Foundation; either
+version 2.1 of the License, or (at your option) any later version.
+
+This library is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+Lesser General Public License for more details.
+
+You should have received a copy of the GNU Lesser General Public
+License along with this library; if not, write to the Free Software
+Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
+
+*Tab=3***********************************************************************/
+
+
+
+#if ! defined (stopwatch_Int64_HEADER_INCLUDED)
+#define	stopwatch_Int64_HEADER_INCLUDED
+
+#if defined (_MSC_VER)
+	#pragma once
+	#pragma warning (4 : 4250) // "Inherits via dominance."
+#endif
+
+
+
+/*\\\ INCLUDE FILES \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+
+
+namespace stopwatch
+{
+
+
+#if defined (_MSC_VER)
+
+	typedef	__int64	Int64;
+
+#elif defined (__MWERKS__) || defined (__GNUC__)
+
+	typedef	long long	Int64;
+
+#elif defined (__BEOS__)
+
+	typedef	int64	Int64;
+
+#else
+
+	#error No 64-bit integer type defined for this compiler !
+
+#endif
+
+
+}	// namespace stopwatch
+
+
+
+#endif	// stopwatch_Int64_HEADER_INCLUDED
+
+
+
+/*\\\ EOF \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
diff --git a/demos/spectrum/fftreal/stopwatch/StopWatch.cpp b/demos/spectrum/fftreal/stopwatch/StopWatch.cpp
new file mode 100644
index 0000000..7795d86
--- /dev/null
+++ b/demos/spectrum/fftreal/stopwatch/StopWatch.cpp
@@ -0,0 +1,101 @@
+/*****************************************************************************
+
+        StopWatch.cpp
+        Copyright (c) 2005 Laurent de Soras
+
+--- Legal stuff ---
+
+This library is free software; you can redistribute it and/or
+modify it under the terms of the GNU Lesser General Public
+License as published by the Free Software Foundation; either
+version 2.1 of the License, or (at your option) any later version.
+
+This library is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+Lesser General Public License for more details.
+
+You should have received a copy of the GNU Lesser General Public
+License along with this library; if not, write to the Free Software
+Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
+
+*Tab=3***********************************************************************/
+
+
+
+#if defined (_MSC_VER)
+	#pragma warning (1 : 4130) // "'operator' : logical operation on address of string constant"
+	#pragma warning (1 : 4223) // "nonstandard extension used : non-lvalue array converted to pointer"
+	#pragma warning (1 : 4705) // "statement has no effect"
+	#pragma warning (1 : 4706) // "assignment within conditional expression"
+	#pragma warning (4 : 4786) // "identifier was truncated to '255' characters in the debug information"
+	#pragma warning (4 : 4800) // "forcing value to bool 'true' or 'false' (performance warning)"
+	#pragma warning (4 : 4355) // "'this' : used in base member initializer list"
+#endif
+
+
+
+/*\\\ INCLUDE FILES \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+#include	"StopWatch.h"
+
+#include	<cassert>
+
+
+
+namespace stopwatch
+{
+
+
+
+/*\\\ PUBLIC \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+
+
+StopWatch::StopWatch ()
+:	_ccc ()
+,	_nbr_laps (0)
+{
+	// Nothing
+}
+
+
+
+double	StopWatch::get_time_total (Int64 nbr_op) const
+{
+	assert (_nbr_laps > 0);
+	assert (nbr_op > 0);
+
+	return (
+		  static_cast <double> (_ccc.get_time_total ())
+	   / (static_cast <double> (nbr_op) * static_cast <double> (_nbr_laps))
+	);
+}
+
+
+
+double	StopWatch::get_time_best_lap (Int64 nbr_op) const
+{
+	assert (nbr_op > 0);
+
+	return (
+		  static_cast <double> (_ccc.get_time_best_lap ())
+		/ static_cast <double> (nbr_op)
+	);
+}
+
+
+
+/*\\\ PROTECTED \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+
+
+/*\\\ PRIVATE \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+
+
+}	// namespace stopwatch
+
+
+
+/*\\\ EOF \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
diff --git a/demos/spectrum/fftreal/stopwatch/StopWatch.h b/demos/spectrum/fftreal/stopwatch/StopWatch.h
new file mode 100644
index 0000000..9cc47e5
--- /dev/null
+++ b/demos/spectrum/fftreal/stopwatch/StopWatch.h
@@ -0,0 +1,110 @@
+/*****************************************************************************
+
+        StopWatch.h
+        Copyright (c) 2005 Laurent de Soras
+
+Utility class based on ClockCycleCounter to measure the unit time of a
+repeated operation.
+
+--- Legal stuff ---
+
+This library is free software; you can redistribute it and/or
+modify it under the terms of the GNU Lesser General Public
+License as published by the Free Software Foundation; either
+version 2.1 of the License, or (at your option) any later version.
+
+This library is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+Lesser General Public License for more details.
+
+You should have received a copy of the GNU Lesser General Public
+License along with this library; if not, write to the Free Software
+Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
+
+*Tab=3***********************************************************************/
+
+
+
+#if ! defined (stopwatch_StopWatch_HEADER_INCLUDED)
+#define	stopwatch_StopWatch_HEADER_INCLUDED
+
+#if defined (_MSC_VER)
+	#pragma once
+	#pragma warning (4 : 4250) // "Inherits via dominance."
+#endif
+
+
+
+/*\\\ INCLUDE FILES \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+#include	"ClockCycleCounter.h"
+
+
+
+namespace stopwatch
+{
+
+
+
+class StopWatch
+{
+
+/*\\\ PUBLIC \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+public:
+
+						StopWatch ();
+
+	stopwatch_FORCEINLINE void
+						start ();
+	stopwatch_FORCEINLINE void
+						stop_lap ();
+
+	double			get_time_total (Int64 nbr_op) const;
+	double			get_time_best_lap (Int64 nbr_op) const;
+
+
+
+/*\\\ PROTECTED \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+protected:
+
+
+
+/*\\\ PRIVATE \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+private:
+
+	ClockCycleCounter
+						_ccc;
+	Int64				_nbr_laps;
+
+
+
+/*\\\ FORBIDDEN MEMBER FUNCTIONS \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+private:
+
+						StopWatch (const StopWatch &other);
+	StopWatch &		operator = (const StopWatch &other);
+	bool				operator == (const StopWatch &other);
+	bool				operator != (const StopWatch &other);
+
+};	// class StopWatch
+
+
+
+}	// namespace stopwatch
+
+
+
+#include	"StopWatch.hpp"
+
+
+
+#endif	// stopwatch_StopWatch_HEADER_INCLUDED
+
+
+
+/*\\\ EOF \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
diff --git a/demos/spectrum/fftreal/stopwatch/StopWatch.hpp b/demos/spectrum/fftreal/stopwatch/StopWatch.hpp
new file mode 100644
index 0000000..74482a7
--- /dev/null
+++ b/demos/spectrum/fftreal/stopwatch/StopWatch.hpp
@@ -0,0 +1,83 @@
+/*****************************************************************************
+
+        StopWatch.hpp
+        Copyright (c) 2005 Laurent de Soras
+
+--- Legal stuff ---
+
+This library is free software; you can redistribute it and/or
+modify it under the terms of the GNU Lesser General Public
+License as published by the Free Software Foundation; either
+version 2.1 of the License, or (at your option) any later version.
+
+This library is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+Lesser General Public License for more details.
+
+You should have received a copy of the GNU Lesser General Public
+License along with this library; if not, write to the Free Software
+Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
+
+*Tab=3***********************************************************************/
+
+
+
+#if defined (stopwatch_StopWatch_CURRENT_CODEHEADER)
+	#error Recursive inclusion of StopWatch code header.
+#endif
+#define	stopwatch_StopWatch_CURRENT_CODEHEADER
+
+#if ! defined (stopwatch_StopWatch_CODEHEADER_INCLUDED)
+#define	stopwatch_StopWatch_CODEHEADER_INCLUDED
+
+
+
+/*\\\ INCLUDE FILES \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+
+
+namespace stopwatch
+{
+
+
+
+/*\\\ PUBLIC \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+
+
+void	StopWatch::start ()
+{
+	_nbr_laps = 0;
+	_ccc.start ();
+}
+
+
+
+void	StopWatch::stop_lap ()
+{
+	_ccc.stop_lap ();
+	++ _nbr_laps;
+}
+
+
+
+/*\\\ PROTECTED \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+
+
+/*\\\ PRIVATE \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+
+
+}	// namespace stopwatch
+
+
+
+#endif	// stopwatch_StopWatch_CODEHEADER_INCLUDED
+
+#undef stopwatch_StopWatch_CURRENT_CODEHEADER
+
+
+
+/*\\\ EOF \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
diff --git a/demos/spectrum/fftreal/stopwatch/def.h b/demos/spectrum/fftreal/stopwatch/def.h
new file mode 100644
index 0000000..81ee6aa
--- /dev/null
+++ b/demos/spectrum/fftreal/stopwatch/def.h
@@ -0,0 +1,65 @@
+/*****************************************************************************
+
+        def.h
+        Copyright (c) 2003 Laurent de Soras
+
+--- Legal stuff ---
+
+This library is free software; you can redistribute it and/or
+modify it under the terms of the GNU Lesser General Public
+License as published by the Free Software Foundation; either
+version 2.1 of the License, or (at your option) any later version.
+
+This library is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+Lesser General Public License for more details.
+
+You should have received a copy of the GNU Lesser General Public
+License along with this library; if not, write to the Free Software
+Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
+
+*Tab=3***********************************************************************/
+
+
+
+#if ! defined (stopwatch_def_HEADER_INCLUDED)
+#define	stopwatch_def_HEADER_INCLUDED
+
+#if defined (_MSC_VER)
+	#pragma once
+	#pragma warning (4 : 4250) // "Inherits via dominance."
+#endif
+
+
+
+/*\\\ INCLUDE FILES \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+
+
+namespace stopwatch
+{
+
+
+
+#if defined (_MSC_VER)
+
+	#define	stopwatch_FORCEINLINE	__forceinline
+
+#else
+
+	#define	stopwatch_FORCEINLINE	inline
+
+#endif
+
+
+
+}	// namespace stopwatch
+
+
+
+#endif	// stopwatch_def_HEADER_INCLUDED
+
+
+
+/*\\\ EOF \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
diff --git a/demos/spectrum/fftreal/stopwatch/fnc.h b/demos/spectrum/fftreal/stopwatch/fnc.h
new file mode 100644
index 0000000..0554535
--- /dev/null
+++ b/demos/spectrum/fftreal/stopwatch/fnc.h
@@ -0,0 +1,67 @@
+/*****************************************************************************
+
+        fnc.h
+        Copyright (c) 2003 Laurent de Soras
+
+--- Legal stuff ---
+
+This library is free software; you can redistribute it and/or
+modify it under the terms of the GNU Lesser General Public
+License as published by the Free Software Foundation; either
+version 2.1 of the License, or (at your option) any later version.
+
+This library is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+Lesser General Public License for more details.
+
+You should have received a copy of the GNU Lesser General Public
+License along with this library; if not, write to the Free Software
+Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
+
+*Tab=3***********************************************************************/
+
+
+
+#if ! defined (stopwatch_fnc_HEADER_INCLUDED)
+#define	stopwatch_fnc_HEADER_INCLUDED
+
+#if defined (_MSC_VER)
+	#pragma once
+	#pragma warning (4 : 4250) // "Inherits via dominance."
+#endif
+
+
+
+/*\\\ INCLUDE FILES \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+
+
+namespace stopwatch
+{
+
+
+
+template <typename T>
+inline T	min (T a, T b);
+
+template <typename T>
+inline T	max (T a, T b);
+
+inline int	round_int (double x);
+
+
+
+}	// namespace rsp
+
+
+
+#include	"fnc.hpp"
+
+
+
+#endif	// stopwatch_fnc_HEADER_INCLUDED
+
+
+
+/*\\\ EOF \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
diff --git a/demos/spectrum/fftreal/stopwatch/fnc.hpp b/demos/spectrum/fftreal/stopwatch/fnc.hpp
new file mode 100644
index 0000000..0ab5949
--- /dev/null
+++ b/demos/spectrum/fftreal/stopwatch/fnc.hpp
@@ -0,0 +1,85 @@
+/*****************************************************************************
+
+        fnc.hpp
+        Copyright (c) 2003 Laurent de Soras
+
+--- Legal stuff ---
+
+This library is free software; you can redistribute it and/or
+modify it under the terms of the GNU Lesser General Public
+License as published by the Free Software Foundation; either
+version 2.1 of the License, or (at your option) any later version.
+
+This library is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+Lesser General Public License for more details.
+
+You should have received a copy of the GNU Lesser General Public
+License along with this library; if not, write to the Free Software
+Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
+
+*Tab=3***********************************************************************/
+
+
+
+#if defined (stopwatch_fnc_CURRENT_CODEHEADER)
+	#error Recursive inclusion of fnc code header.
+#endif
+#define	stopwatch_fnc_CURRENT_CODEHEADER
+
+#if ! defined (stopwatch_fnc_CODEHEADER_INCLUDED)
+#define	stopwatch_fnc_CODEHEADER_INCLUDED
+
+
+
+/*\\\ INCLUDE FILES \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+#include	<cassert>
+#include	<cmath>
+
+namespace std {}
+
+
+
+namespace stopwatch
+{
+
+
+
+template <typename T>
+inline T	min (T a, T b)
+{
+	return ((a < b) ? a : b);
+}
+
+
+
+template <typename T>
+inline T	max (T a, T b)
+{
+	return ((b < a) ? a : b);
+}
+
+
+
+int	round_int (double x)
+{
+	using namespace std;
+
+	return (static_cast <int> (floor (x + 0.5)));
+}
+
+
+
+}	// namespace stopwatch
+
+
+
+#endif	// stopwatch_fnc_CODEHEADER_INCLUDED
+
+#undef stopwatch_fnc_CURRENT_CODEHEADER
+
+
+
+/*\\\ EOF \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
diff --git a/demos/spectrum/fftreal/test.cpp b/demos/spectrum/fftreal/test.cpp
new file mode 100644
index 0000000..7b6ed2c
--- /dev/null
+++ b/demos/spectrum/fftreal/test.cpp
@@ -0,0 +1,267 @@
+/*****************************************************************************
+
+        test.cpp
+        Copyright (c) 2005 Laurent de Soras
+
+--- Legal stuff ---
+
+This library is free software; you can redistribute it and/or
+modify it under the terms of the GNU Lesser General Public
+License as published by the Free Software Foundation; either
+version 2.1 of the License, or (at your option) any later version.
+
+This library is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+Lesser General Public License for more details.
+
+You should have received a copy of the GNU Lesser General Public
+License along with this library; if not, write to the Free Software
+Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
+
+*Tab=3***********************************************************************/
+
+
+
+#if defined (_MSC_VER)
+	#pragma warning (4 : 4786) // "identifier was truncated to '255' characters in the debug information"
+	#pragma warning (4 : 4800) // "forcing value to bool 'true' or 'false' (performance warning)"
+#endif
+
+
+
+/*\\\ INCLUDE FILES \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+#include	"test_settings.h"
+#include	"TestHelperFixLen.h"
+#include	"TestHelperNormal.h"
+
+#if defined (_MSC_VER)
+#include	<crtdbg.h>
+#include	<new.h>
+#endif	// _MSC_VER
+
+#include	<new>
+
+#include	<cassert>
+#include	<cstdio>
+
+
+
+#define	TEST_
+
+
+/*\\\ FUNCTIONS \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+
+
+static int	TEST_perform_test_accuracy_all ();
+static int	TEST_perform_test_speed_all ();
+
+static void	TEST_prog_init ();
+static void	TEST_prog_end ();
+
+
+
+int main (int argc, char *argv [])
+{
+	using namespace std;
+
+	int				ret_val = 0;
+
+	TEST_prog_init ();
+
+	try
+	{
+		if (ret_val == 0)
+		{
+			ret_val = TEST_perform_test_accuracy_all ();
+		}
+
+		if (ret_val == 0)
+		{
+			ret_val = TEST_perform_test_speed_all ();
+		}
+	}
+
+	catch (std::exception &e)
+	{
+		printf ("\n*** main(): Exception (std::exception) : %s\n", e.what ());
+		ret_val = -1;
+	}
+
+	catch (...)
+	{
+		printf ("\n*** main(): Undefined exception\n");
+		ret_val = -1;
+	}
+
+	TEST_prog_end ();
+
+	return (ret_val);
+}
+
+
+
+int	TEST_perform_test_accuracy_all ()
+{
+   int            ret_val = 0;
+
+	TestHelperNormal <float >::perform_test_accuracy (ret_val);
+	TestHelperNormal <double>::perform_test_accuracy (ret_val);
+
+   TestHelperFixLen < 1>::perform_test_accuracy (ret_val);
+   TestHelperFixLen < 2>::perform_test_accuracy (ret_val);
+   TestHelperFixLen < 3>::perform_test_accuracy (ret_val);
+   TestHelperFixLen < 4>::perform_test_accuracy (ret_val);
+   TestHelperFixLen < 7>::perform_test_accuracy (ret_val);
+   TestHelperFixLen < 8>::perform_test_accuracy (ret_val);
+   TestHelperFixLen <10>::perform_test_accuracy (ret_val);
+   TestHelperFixLen <12>::perform_test_accuracy (ret_val);
+   TestHelperFixLen <13>::perform_test_accuracy (ret_val);
+
+	return (ret_val);
+}
+
+
+
+int	TEST_perform_test_speed_all ()
+{
+   int            ret_val = 0;
+
+#if defined (test_settings_SPEED_TEST_ENABLED)
+
+	TestHelperNormal <float >::perform_test_speed (ret_val);
+	TestHelperNormal <double>::perform_test_speed (ret_val);
+
+   TestHelperFixLen < 1>::perform_test_speed (ret_val);
+   TestHelperFixLen < 2>::perform_test_speed (ret_val);
+   TestHelperFixLen < 3>::perform_test_speed (ret_val);
+   TestHelperFixLen < 4>::perform_test_speed (ret_val);
+   TestHelperFixLen < 7>::perform_test_speed (ret_val);
+   TestHelperFixLen < 8>::perform_test_speed (ret_val);
+   TestHelperFixLen <10>::perform_test_speed (ret_val);
+   TestHelperFixLen <12>::perform_test_speed (ret_val);
+   TestHelperFixLen <14>::perform_test_speed (ret_val);
+   TestHelperFixLen <16>::perform_test_speed (ret_val);
+   TestHelperFixLen <20>::perform_test_speed (ret_val);
+
+#endif
+
+   return (ret_val);
+}
+
+
+
+#if defined (_MSC_VER)
+static int __cdecl	TEST_new_handler_cb (size_t dummy)
+{
+	throw std::bad_alloc ();
+	return (0);
+}
+#endif	// _MSC_VER
+
+
+
+#if defined (_MSC_VER) && ! defined (NDEBUG)
+static int	__cdecl	TEST_debug_alloc_hook_cb (int alloc_type, void *user_data_ptr, size_t size, int block_type, long request_nbr, const unsigned char *filename_0, int line_nbr)
+{
+	if (block_type != _CRT_BLOCK)	// Ignore CRT blocks to prevent infinite recursion
+	{
+		switch (alloc_type)
+		{
+		case	_HOOK_ALLOC:
+		case	_HOOK_REALLOC:
+		case	_HOOK_FREE:
+
+			// Put some debug code here
+
+			break;
+
+		default:
+			assert (false);	// Undefined allocation type
+			break;
+		}
+	}
+
+	return (1);
+}
+#endif
+
+
+
+#if defined (_MSC_VER) && ! defined (NDEBUG)
+static int	__cdecl	TEST_debug_report_hook_cb (int report_type, char *user_msg_0, int *ret_val_ptr)
+{
+	*ret_val_ptr = 0;	// 1 to override the CRT default reporting mode
+
+	switch (report_type)
+	{
+	case	_CRT_WARN:
+	case	_CRT_ERROR:
+	case	_CRT_ASSERT:
+
+// Put some debug code here
+
+		break;
+	}
+
+	return (*ret_val_ptr);
+}
+#endif
+
+
+
+static void	TEST_prog_init ()
+{
+#if defined (_MSC_VER)
+	::_set_new_handler (::TEST_new_handler_cb);
+#endif	// _MSC_VER
+
+#if defined (_MSC_VER) && ! defined (NDEBUG)
+	{
+		const int	mode =   (1 * _CRTDBG_MODE_DEBUG)
+						       | (1 * _CRTDBG_MODE_WNDW);
+		::_CrtSetReportMode (_CRT_WARN, mode);
+		::_CrtSetReportMode (_CRT_ERROR, mode);
+		::_CrtSetReportMode (_CRT_ASSERT, mode);
+
+		const int	old_flags = ::_CrtSetDbgFlag (_CRTDBG_REPORT_FLAG);
+		::_CrtSetDbgFlag (  old_flags
+		                  | (1 * _CRTDBG_LEAK_CHECK_DF)
+		                  | (1 * _CRTDBG_CHECK_ALWAYS_DF));
+		::_CrtSetBreakAlloc (-1);	// Specify here a memory bloc number
+		::_CrtSetAllocHook (TEST_debug_alloc_hook_cb);
+		::_CrtSetReportHook (TEST_debug_report_hook_cb);
+
+		// Speed up I/O but breaks C stdio compatibility
+//		std::cout.sync_with_stdio (false);
+//		std::cin.sync_with_stdio (false);
+//		std::cerr.sync_with_stdio (false);
+//		std::clog.sync_with_stdio (false);
+	}
+#endif	// _MSC_VER, NDEBUG
+}
+
+
+
+static void	TEST_prog_end ()
+{
+#if defined (_MSC_VER) && ! defined (NDEBUG)
+	{
+		const int	mode =   (1 * _CRTDBG_MODE_DEBUG)
+						       | (0 * _CRTDBG_MODE_WNDW);
+		::_CrtSetReportMode (_CRT_WARN, mode);
+		::_CrtSetReportMode (_CRT_ERROR, mode);
+		::_CrtSetReportMode (_CRT_ASSERT, mode);
+
+		::_CrtMemState	mem_state;
+		::_CrtMemCheckpoint (&mem_state);
+		::_CrtMemDumpStatistics (&mem_state);
+	}
+#endif	// _MSC_VER, NDEBUG
+}
+
+
+
+/*\\\ EOF \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
diff --git a/demos/spectrum/fftreal/test_fnc.h b/demos/spectrum/fftreal/test_fnc.h
new file mode 100644
index 0000000..2622156
--- /dev/null
+++ b/demos/spectrum/fftreal/test_fnc.h
@@ -0,0 +1,53 @@
+/*****************************************************************************
+
+        test_fnc.h
+        Copyright (c) 2005 Laurent de Soras
+
+--- Legal stuff ---
+
+This library is free software; you can redistribute it and/or
+modify it under the terms of the GNU Lesser General Public
+License as published by the Free Software Foundation; either
+version 2.1 of the License, or (at your option) any later version.
+
+This library is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+Lesser General Public License for more details.
+
+You should have received a copy of the GNU Lesser General Public
+License along with this library; if not, write to the Free Software
+Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
+
+*Tab=3***********************************************************************/
+
+
+
+#if ! defined (test_fnc_HEADER_INCLUDED)
+#define	test_fnc_HEADER_INCLUDED
+
+#if defined (_MSC_VER)
+	#pragma once
+	#pragma warning (4 : 4250) // "Inherits via dominance."
+#endif
+
+
+
+/*\\\ INCLUDE FILES \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+
+
+template <class T>
+inline T	limit (const T &x, const T &inf, const T &sup);
+
+
+
+#include	"test_fnc.hpp"
+
+
+
+#endif	// test_fnc_HEADER_INCLUDED
+
+
+
+/*\\\ EOF \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
diff --git a/demos/spectrum/fftreal/test_fnc.hpp b/demos/spectrum/fftreal/test_fnc.hpp
new file mode 100644
index 0000000..4b5f9f5
--- /dev/null
+++ b/demos/spectrum/fftreal/test_fnc.hpp
@@ -0,0 +1,56 @@
+/*****************************************************************************
+
+        test_fnc.hpp
+        Copyright (c) 2005 Laurent de Soras
+
+--- Legal stuff ---
+
+This library is free software; you can redistribute it and/or
+modify it under the terms of the GNU Lesser General Public
+License as published by the Free Software Foundation; either
+version 2.1 of the License, or (at your option) any later version.
+
+This library is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+Lesser General Public License for more details.
+
+You should have received a copy of the GNU Lesser General Public
+License along with this library; if not, write to the Free Software
+Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
+
+*Tab=3***********************************************************************/
+
+
+
+#if defined (test_fnc_CURRENT_CODEHEADER)
+	#error Recursive inclusion of test_fnc code header.
+#endif
+#define	test_fnc_CURRENT_CODEHEADER
+
+#if ! defined (test_fnc_CODEHEADER_INCLUDED)
+#define	test_fnc_CODEHEADER_INCLUDED
+
+
+
+/*\\\ INCLUDE FILES \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+
+
+template <class T>
+T	limit (const T &x, const T &inf, const T &sup)
+{
+	assert (! (sup < inf));
+
+	return ((x < inf) ? inf : ((sup < x) ? sup : x));
+}
+
+
+
+#endif	// test_fnc_CODEHEADER_INCLUDED
+
+#undef test_fnc_CURRENT_CODEHEADER
+
+
+
+/*\\\ EOF \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
diff --git a/demos/spectrum/fftreal/test_settings.h b/demos/spectrum/fftreal/test_settings.h
new file mode 100644
index 0000000..b893afc
--- /dev/null
+++ b/demos/spectrum/fftreal/test_settings.h
@@ -0,0 +1,45 @@
+/*****************************************************************************
+
+        test_settings.h
+        Copyright (c) 2005 Laurent de Soras
+
+--- Legal stuff ---
+
+This library is free software; you can redistribute it and/or
+modify it under the terms of the GNU Lesser General Public
+License as published by the Free Software Foundation; either
+version 2.1 of the License, or (at your option) any later version.
+
+This library is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+Lesser General Public License for more details.
+
+You should have received a copy of the GNU Lesser General Public
+License along with this library; if not, write to the Free Software
+Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
+
+*Tab=3***********************************************************************/
+
+
+
+#if ! defined (test_settings_HEADER_INCLUDED)
+#define	test_settings_HEADER_INCLUDED
+
+#if defined (_MSC_VER)
+	#pragma once
+	#pragma warning (4 : 4250) // "Inherits via dominance."
+#endif
+
+
+
+// #undef this label to avoid speed test compilation.
+#define	test_settings_SPEED_TEST_ENABLED
+
+
+
+#endif	// test_settings_HEADER_INCLUDED
+
+
+
+/*\\\ EOF \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
diff --git a/demos/spectrum/fftreal/testapp.dpr b/demos/spectrum/fftreal/testapp.dpr
new file mode 100644
index 0000000..54f2eb9
--- /dev/null
+++ b/demos/spectrum/fftreal/testapp.dpr
@@ -0,0 +1,150 @@
+program testapp;
+{$APPTYPE CONSOLE}
+uses
+  SysUtils,
+  fftreal in 'fftreal.pas',
+  Math,
+  Windows;
+
+var
+   nbr_points  : longint;
+   x, f        : pflt_array;
+   fft         : TFFTReal;
+   i           : longint;
+   PI          : double;
+   areal, img  : double;
+   f_abs       : double;
+   buffer_size : longint;
+   nbr_tests   : longint;
+   time0, time1, time2 : int64;
+   timereso    : int64;
+   offset      : longint;
+   t0, t1      : double;
+   nbr_s_chn   : longint;
+   tempp1, tempp2 : pflt_array;
+
+begin
+  (*______________________________________________
+   *
+   * Exactness test
+   *______________________________________________
+   *)
+
+  WriteLn('Accuracy test:');
+  WriteLn;
+
+  nbr_points := 16;       // Power of 2
+  GetMem(x, nbr_points * sizeof_flt);
+  GetMem(f, nbr_points * sizeof_flt);
+  fft := TFFTReal.Create(nbr_points);    // FFT object initialized here
+
+  // Test signal
+  PI := ArcTan(1) * 4;
+  for i := 0 to nbr_points-1 do
+  begin
+    x^[i] := -1 + sin (3*2*PI*i/nbr_points)
+                + cos (5*2*PI*i/nbr_points) * 2
+                - sin (7*2*PI*i/nbr_points) * 3
+                + cos (8*2*PI*i/nbr_points) * 5;
+  end;
+
+  // Compute FFT and IFFT
+  fft.do_fft(f, x);
+  fft.do_ifft(f, x);
+  fft.rescale(x);
+
+  // Display the result
+  WriteLn('FFT:');
+  for i := 0 to nbr_points div 2 do
+  begin
+    areal := f^[i];
+    if (i > 0) and (i < nbr_points div 2) then
+      img := f^[i + nbr_points div 2]
+    else
+      img := 0;
+
+    f_abs := Sqrt(areal * areal + img * img);
+    WriteLn(Format('%5d: %12.6f %12.6f (%12.6f)', [i, areal, img, f_abs]));
+  end;
+
+  WriteLn;
+  WriteLn('IFFT:');
+  for i := 0 to nbr_points-1 do
+    WriteLn(Format('%5d: %f', [i, x^[i]]));
+
+  WriteLn;
+
+  FreeMem(x);
+  FreeMem(f);
+  fft.Free;
+
+
+  (*______________________________________________
+   *
+   * Speed test
+   *______________________________________________
+   *)
+
+  WriteLn('Speed test:');
+  WriteLn('Please wait...');
+  WriteLn;
+
+  nbr_points := 1024;	          // Power of 2
+  buffer_size := 256*nbr_points;  // Number of flt_t (float or double)
+  nbr_tests := 10000;
+
+  assert(nbr_points <= buffer_size);
+  GetMem(x, buffer_size * sizeof_flt);
+  GetMem(f, buffer_size * sizeof_flt);
+  fft := TFFTReal.Create(nbr_points);					// FFT object initialized here
+
+  // Test signal: noise
+  for i := 0 to nbr_points-1 do
+    x^[i] := Random($7fff) - ($7fff shr 1);
+
+  // timing
+  QueryPerformanceFrequency(timereso);
+  QueryPerformanceCounter(time0);
+
+  for i := 0 to nbr_tests-1 do
+  begin
+    offset := (i * nbr_points) and (buffer_size - 1);
+    tempp1 := f;
+    inc(tempp1, offset);
+    tempp2 := x;
+    inc(tempp2, offset);
+    fft.do_fft(tempp1, tempp2);
+  end;
+
+  QueryPerformanceCounter(time1);
+
+  for i := 0 to nbr_tests-1 do
+  begin
+    offset := (i * nbr_points) and (buffer_size - 1);
+    tempp1 := f;
+    inc(tempp1, offset);
+    tempp2 := x;
+    inc(tempp2, offset);
+    fft.do_ifft(tempp1, tempp2);
+    fft.rescale(x);
+  end;
+
+  QueryPerformanceCounter(time2);
+
+  t0 := ((time1-time0) / timereso) / nbr_tests;
+  t1 := ((time2-time1) / timereso) / nbr_tests;
+
+  WriteLn(Format('%d-points FFT           : %.0f us.', [nbr_points, t0 * 1000000]));
+  WriteLn(Format('%d-points IFFT + scaling: %.0f us.', [nbr_points, t1 * 1000000]));
+
+  nbr_s_chn := Floor(nbr_points / ((t0 + t1) * 44100 * 2));
+  WriteLn(Format('Peak performance: FFT+IFFT on %d mono channels at 44.1 KHz (with overlapping)', [nbr_s_chn]));
+  WriteLn;
+
+  FreeMem(x);
+  FreeMem(f);
+  fft.Free;
+
+  WriteLn('Press [Return] key to terminate...');
+  ReadLn;
+end.