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-\section{\module{audioop} ---
-         Manipulate raw audio data}
-
-\declaremodule{builtin}{audioop}
-\modulesynopsis{Manipulate raw audio data.}
-
-
-The \module{audioop} module contains some useful operations on sound
-fragments.  It operates on sound fragments consisting of signed
-integer samples 8, 16 or 32 bits wide, stored in Python strings.
-All scalar items are integers, unless specified otherwise.
-
-% This para is mostly here to provide an excuse for the index entries...
-This module provides support for a-LAW, u-LAW and Intel/DVI ADPCM encodings.
-\index{Intel/DVI ADPCM}
-\index{ADPCM, Intel/DVI}
-\index{a-LAW}
-\index{u-LAW}
-
-A few of the more complicated operations only take 16-bit samples,
-otherwise the sample size (in bytes) is always a parameter of the
-operation.
-
-The module defines the following variables and functions:
-
-\begin{excdesc}{error}
-This exception is raised on all errors, such as unknown number of bytes
-per sample, etc.
-\end{excdesc}
-
-\begin{funcdesc}{add}{fragment1, fragment2, width}
-Return a fragment which is the addition of the two samples passed as
-parameters.  \var{width} is the sample width in bytes, either
-\code{1}, \code{2} or \code{4}.  Both fragments should have the same
-length.
-\end{funcdesc}
-
-\begin{funcdesc}{adpcm2lin}{adpcmfragment, width, state}
-Decode an Intel/DVI ADPCM coded fragment to a linear fragment.  See
-the description of \function{lin2adpcm()} for details on ADPCM coding.
-Return a tuple \code{(\var{sample}, \var{newstate})} where the sample
-has the width specified in \var{width}.
-\end{funcdesc}
-
-\begin{funcdesc}{alaw2lin}{fragment, width}
-Convert sound fragments in a-LAW encoding to linearly encoded sound
-fragments.  a-LAW encoding always uses 8 bits samples, so \var{width}
-refers only to the sample width of the output fragment here.
-\versionadded{2.5}
-\end{funcdesc}
-
-\begin{funcdesc}{avg}{fragment, width}
-Return the average over all samples in the fragment.
-\end{funcdesc}
-
-\begin{funcdesc}{avgpp}{fragment, width}
-Return the average peak-peak value over all samples in the fragment.
-No filtering is done, so the usefulness of this routine is
-questionable.
-\end{funcdesc}
-
-\begin{funcdesc}{bias}{fragment, width, bias}
-Return a fragment that is the original fragment with a bias added to
-each sample.
-\end{funcdesc}
-
-\begin{funcdesc}{cross}{fragment, width}
-Return the number of zero crossings in the fragment passed as an
-argument.
-\end{funcdesc}
-
-\begin{funcdesc}{findfactor}{fragment, reference}
-Return a factor \var{F} such that
-\code{rms(add(\var{fragment}, mul(\var{reference}, -\var{F})))} is
-minimal, i.e., return the factor with which you should multiply
-\var{reference} to make it match as well as possible to
-\var{fragment}.  The fragments should both contain 2-byte samples.
-
-The time taken by this routine is proportional to
-\code{len(\var{fragment})}.
-\end{funcdesc}
-
-\begin{funcdesc}{findfit}{fragment, reference}
-Try to match \var{reference} as well as possible to a portion of
-\var{fragment} (which should be the longer fragment).  This is
-(conceptually) done by taking slices out of \var{fragment}, using
-\function{findfactor()} to compute the best match, and minimizing the
-result.  The fragments should both contain 2-byte samples.  Return a
-tuple \code{(\var{offset}, \var{factor})} where \var{offset} is the
-(integer) offset into \var{fragment} where the optimal match started
-and \var{factor} is the (floating-point) factor as per
-\function{findfactor()}.
-\end{funcdesc}
-
-\begin{funcdesc}{findmax}{fragment, length}
-Search \var{fragment} for a slice of length \var{length} samples (not
-bytes!)\ with maximum energy, i.e., return \var{i} for which
-\code{rms(fragment[i*2:(i+length)*2])} is maximal.  The fragments
-should both contain 2-byte samples.
-
-The routine takes time proportional to \code{len(\var{fragment})}.
-\end{funcdesc}
-
-\begin{funcdesc}{getsample}{fragment, width, index}
-Return the value of sample \var{index} from the fragment.
-\end{funcdesc}
-
-\begin{funcdesc}{lin2adpcm}{fragment, width, state}
-Convert samples to 4 bit Intel/DVI ADPCM encoding.  ADPCM coding is an
-adaptive coding scheme, whereby each 4 bit number is the difference
-between one sample and the next, divided by a (varying) step.  The
-Intel/DVI ADPCM algorithm has been selected for use by the IMA, so it
-may well become a standard.
-
-\var{state} is a tuple containing the state of the coder.  The coder
-returns a tuple \code{(\var{adpcmfrag}, \var{newstate})}, and the
-\var{newstate} should be passed to the next call of
-\function{lin2adpcm()}.  In the initial call, \code{None} can be
-passed as the state.  \var{adpcmfrag} is the ADPCM coded fragment
-packed 2 4-bit values per byte.
-\end{funcdesc}
-
-\begin{funcdesc}{lin2alaw}{fragment, width}
-Convert samples in the audio fragment to a-LAW encoding and return
-this as a Python string.  a-LAW is an audio encoding format whereby
-you get a dynamic range of about 13 bits using only 8 bit samples.  It
-is used by the Sun audio hardware, among others.
-\versionadded{2.5}
-\end{funcdesc}
-
-\begin{funcdesc}{lin2lin}{fragment, width, newwidth}
-Convert samples between 1-, 2- and 4-byte formats.
-\end{funcdesc}
-
-\begin{funcdesc}{lin2ulaw}{fragment, width}
-Convert samples in the audio fragment to u-LAW encoding and return
-this as a Python string.  u-LAW is an audio encoding format whereby
-you get a dynamic range of about 14 bits using only 8 bit samples.  It
-is used by the Sun audio hardware, among others.
-\end{funcdesc}
-
-\begin{funcdesc}{minmax}{fragment, width}
-Return a tuple consisting of the minimum and maximum values of all
-samples in the sound fragment.
-\end{funcdesc}
-
-\begin{funcdesc}{max}{fragment, width}
-Return the maximum of the \emph{absolute value} of all samples in a
-fragment.
-\end{funcdesc}
-
-\begin{funcdesc}{maxpp}{fragment, width}
-Return the maximum peak-peak value in the sound fragment.
-\end{funcdesc}
-
-\begin{funcdesc}{mul}{fragment, width, factor}
-Return a fragment that has all samples in the original fragment
-multiplied by the floating-point value \var{factor}.  Overflow is
-silently ignored.
-\end{funcdesc}
-
-\begin{funcdesc}{ratecv}{fragment, width, nchannels, inrate, outrate,
-                         state\optional{, weightA\optional{, weightB}}}
-Convert the frame rate of the input fragment.
-
-\var{state} is a tuple containing the state of the converter.  The
-converter returns a tuple \code{(\var{newfragment}, \var{newstate})},
-and \var{newstate} should be passed to the next call of
-\function{ratecv()}.  The initial call should pass \code{None}
-as the state.
-
-The \var{weightA} and \var{weightB} arguments are parameters for a
-simple digital filter and default to \code{1} and \code{0} respectively.
-\end{funcdesc}
-
-\begin{funcdesc}{reverse}{fragment, width}
-Reverse the samples in a fragment and returns the modified fragment.
-\end{funcdesc}
-
-\begin{funcdesc}{rms}{fragment, width}
-Return the root-mean-square of the fragment, i.e.
-\begin{displaymath}
-\catcode`_=8
-\sqrt{\frac{\sum{{S_{i}}^{2}}}{n}}
-\end{displaymath}
-This is a measure of the power in an audio signal.
-\end{funcdesc}
-
-\begin{funcdesc}{tomono}{fragment, width, lfactor, rfactor} 
-Convert a stereo fragment to a mono fragment.  The left channel is
-multiplied by \var{lfactor} and the right channel by \var{rfactor}
-before adding the two channels to give a mono signal.
-\end{funcdesc}
-
-\begin{funcdesc}{tostereo}{fragment, width, lfactor, rfactor}
-Generate a stereo fragment from a mono fragment.  Each pair of samples
-in the stereo fragment are computed from the mono sample, whereby left
-channel samples are multiplied by \var{lfactor} and right channel
-samples by \var{rfactor}.
-\end{funcdesc}
-
-\begin{funcdesc}{ulaw2lin}{fragment, width}
-Convert sound fragments in u-LAW encoding to linearly encoded sound
-fragments.  u-LAW encoding always uses 8 bits samples, so \var{width}
-refers only to the sample width of the output fragment here.
-\end{funcdesc}
-
-Note that operations such as \function{mul()} or \function{max()} make
-no distinction between mono and stereo fragments, i.e.\ all samples
-are treated equal.  If this is a problem the stereo fragment should be
-split into two mono fragments first and recombined later.  Here is an
-example of how to do that:
-
-\begin{verbatim}
-def mul_stereo(sample, width, lfactor, rfactor):
-    lsample = audioop.tomono(sample, width, 1, 0)
-    rsample = audioop.tomono(sample, width, 0, 1)
-    lsample = audioop.mul(sample, width, lfactor)
-    rsample = audioop.mul(sample, width, rfactor)
-    lsample = audioop.tostereo(lsample, width, 1, 0)
-    rsample = audioop.tostereo(rsample, width, 0, 1)
-    return audioop.add(lsample, rsample, width)
-\end{verbatim}
-
-If you use the ADPCM coder to build network packets and you want your
-protocol to be stateless (i.e.\ to be able to tolerate packet loss)
-you should not only transmit the data but also the state.  Note that
-you should send the \var{initial} state (the one you passed to
-\function{lin2adpcm()}) along to the decoder, not the final state (as
-returned by the coder).  If you want to use \function{struct.struct()}
-to store the state in binary you can code the first element (the
-predicted value) in 16 bits and the second (the delta index) in 8.
-
-The ADPCM coders have never been tried against other ADPCM coders,
-only against themselves.  It could well be that I misinterpreted the
-standards in which case they will not be interoperable with the
-respective standards.
-
-The \function{find*()} routines might look a bit funny at first sight.
-They are primarily meant to do echo cancellation.  A reasonably
-fast way to do this is to pick the most energetic piece of the output
-sample, locate that in the input sample and subtract the whole output
-sample from the input sample:
-
-\begin{verbatim}
-def echocancel(outputdata, inputdata):
-    pos = audioop.findmax(outputdata, 800)    # one tenth second
-    out_test = outputdata[pos*2:]
-    in_test = inputdata[pos*2:]
-    ipos, factor = audioop.findfit(in_test, out_test)
-    # Optional (for better cancellation):
-    # factor = audioop.findfactor(in_test[ipos*2:ipos*2+len(out_test)], 
-    #              out_test)
-    prefill = '\0'*(pos+ipos)*2
-    postfill = '\0'*(len(inputdata)-len(prefill)-len(outputdata))
-    outputdata = prefill + audioop.mul(outputdata,2,-factor) + postfill
-    return audioop.add(inputdata, outputdata, 2)
-\end{verbatim}