\section{Built-in module \sectcode{audioop}}
\bimodindex{audioop}

The audioop module contains some useful operations on sound fragments.
It operates on sound fragments consisting of signed integer samples of
8, 16 or 32 bits wide, stored in Python strings.  This is the same
format as used by the \code{al} and \code{sunaudiodev} modules.  All
scalar items are integers, unless specified otherwise.

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:

\renewcommand{\indexsubitem}{(in module audioop)}
\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}
This function returns a fragment that 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}
This routine decodes an Intel/DVI ADPCM coded fragment to a linear
fragment. See the description of \code{lin2adpcm} for details on ADPCM
coding. The routine returns a tuple
\code{(\var{sample}, \var{newstate})}
where the sample has the width specified in \var{width}.
\end{funcdesc}

\begin{funcdesc}{adpcm32lin}{adpcmfragment\, width\, state}
This routine decodes an alternative 3-bit ADPCM code. See
\code{lin2adpcm3} for details.
\end{funcdesc}

\begin{funcdesc}{avg}{fragment\, width}
This function returns the average over all samples in the fragment.
\end{funcdesc}

\begin{funcdesc}{avgpp}{fragment\, width}
This function returns 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}
This function returns a fragment that is the original fragment with a
bias added to each sample.
\end{funcdesc}

\begin{funcdesc}{cross}{fragment\, width}
This function returns the number of zero crossings in the fragment
passed as an argument.
\end{funcdesc}

\begin{funcdesc}{findfactor}{fragment\, reference}
This routine (which only accepts 2-byte sample fragments) calculates a
factor \var{F} such that \code{rms(add(fragment, mul(reference, -F)))}
is minimal, i.e. it calculates the factor with which you should
multiply \var{reference} to make it match as good as possible to
\var{fragment}. The fragments should be the same size.

The time taken by this routine is proportional to \code{len(fragment)}. 
\end{funcdesc}

\begin{funcdesc}{findfit}{fragment\, reference}
This routine (which only accepts 2-byte sample fragments) tries to
match \var{reference} as good as possible to a portion of
\var{fragment} (which should be the longer fragment). It
(conceptually) does this by taking slices out of \var{fragment}, using
\code{findfactor} to compute the best match, and minimizing the
result.
It returns a tuple \code{(\var{offset}, \var{factor})} with \var{offset} the
(integer) offset into \var{fragment} where the optimal match started
and \var{factor} the floating-point factor as per \code{findfactor}.
\end{funcdesc}

\begin{funcdesc}{findmax}{fragment\, length}
This routine (which only accepts 2-byte sample fragments) searches
\var{fragment} for a slice of length \var{length} samples (not bytes!)
with maximum energy, i.e. it returns \var{i} for which
\code{rms(fragment[i*2:(i+length)*2])} is maximal.

The routine takes time proportional to \code{len(fragment)}.
\end{funcdesc}

\begin{funcdesc}{getsample}{fragment\, width\, index}
This function returns the value of sample \var{index} from the
fragment.
\end{funcdesc}

\begin{funcdesc}{lin2lin}{fragment\, width\, newwidth}
This function converts samples between 1-, 2- and 4-byte formats.
\end{funcdesc}

\begin{funcdesc}{lin2adpcm}{fragment\, width\, state}
This function converts 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.

\code{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 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}{lin2adpcm3}{fragment\, width\, state}
This is an alternative ADPCM coder that uses only 3 bits per sample.
It is not compatible with the Intel/DVI ADPCM coder and its output is
not packed (due to laziness on the side of the author). Its use is
discouraged.
\end{funcdesc}

\begin{funcdesc}{lin2ulaw}{fragment\, width}
This function converts samples in the audio fragment to U-LAW encoding
and returns 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}
This function returns a tuple consisting of the minimum and maximum
values of all samples in the sound fragment.
\end{funcdesc}

\begin{funcdesc}{max}{fragment\, width}
This function returns the maximum of the {\em absolute value} of all
samples in a fragment.
\end{funcdesc}

\begin{funcdesc}{maxpp}{fragment\, width}
This function returns the maximum peak-peak value in the sound fragment.
\end{funcdesc}

\begin{funcdesc}{mul}{fragment\, width\, factor}
Mul returns a fragment that has all samples in the original framgent
multiplied by the floating-point value \var{factor}. Overflow is
silently ignored.
\end{funcdesc}

\begin{funcdesc}{reverse}{fragment\, width}
This function reverses the samples in a fragment and returns the
modified fragment.
\end{funcdesc}

\begin{funcdesc}{tomono}{fragment\, width\, lfactor\, rfactor} 
This function converts 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}
This function generates 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}{mul}{fragment\, width\, factor}
Mul returns a fragment that has all samples in the original framgent
multiplied by the floating-point value \var{factor}. Overflow is
silently ignored.
\end{funcdesc}

\begin{funcdesc}{rms}{fragment\, width\, factor}
Returns the root-mean-square of the fragment, i.e.
\iftexi
the square root of the quotient of the sum of all squared sample value,
divided by the sumber of samples.
\else
% in eqn: sqrt { sum S sub i sup 2  over n }
\begin{displaymath}
\catcode`_=8
\sqrt{\frac{\sum{{S_{i}}^{2}}}{n}}
\end{displaymath}
\fi
This is a measure of the power in an audio signal.
\end{funcdesc}

\begin{funcdesc}{ulaw2lin}{fragment\, width}
This function converts sound fragments in ULAW encoding to linearly
encoded sound fragments. ULAW 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 \code{mul} or \code{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:
\bcode\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}\ecode

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
lin2adpcm) along to the decoder, not the final state (as returned by
the coder). If you want to use \code{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 \code{find...} routines might look a bit funny at first sight.
They are primarily meant for doing 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:
\bcode\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}\ecode
