<chapter>
<title>Signal Processing</title>
<para>
The &est signal processing library provides a set of standard
signal processing tools designed specifically for speech
analysis. The library includes:
<itemizedlist>
<listitem><para>Windowing (creating frames from a continuous waveform)</para></listitem>
<listitem><para>Linear prediction and associated operations</para></listitem>
<listitem><para>Cepstral analysis, both via lpc and DFT.</para></listitem>
<listitem><para>Filterbank analysis</para></listitem>
<listitem><para>Frequency warping including mel-scaling</para></listitem>
<listitem><para>Pitch tracking</para></listitem>
<listitem><para>Energy and Power analysis</para></listitem>
<listitem><para>Spectrogram Generation</para></listitem>
<listitem><para>Fourier Transforms</para></listitem>
<listitem><para>Pitchmarking (of laryngograph signals)</para></listitem>
</itemizedlist>
</para>
<sect1>
<title>Overview</title>
<sect2><title>Design Issues</title>
<para>
The signal processing library is designed specifically for speech
applications and hence all functions are written with that end
goal in mind. The design of the library has centered around
building a set of commonly used easy to configure analysis
routines.
</para>
<para>
<variablelist>
<varlistentry><term>Speed</term><listitem>
<para>We have tried to make the functions as fast as
possible. Signal processing can often be time critical, and
so it will always be the case that if the code for a
particular signal processing algroithm is written in a
single function loop it will run faster than by using
libraries.
</para> <para>
However, the signal processing routines in the EST library
are in general very fast, and the fact that they use
classes such as EST_Track and EST_FVector does not make
them slower than they would be if float * etc was used.
</para></listitem> </varlistentry>
<varlistentry><term>types</term><listitem>
<para>The library makes heavy use of a small number of
classes, specifically <link linkend="EST-Wave">
EST_Wave</link> <link linkend="EST-Track">
EST_Track</link> and <link linkend="EST-FVector">
EST_FVector</link>. These classes are basically arrays
and matrices, but take care of issues such as memory
managment, error handling and file i/o. Using these
classes in the library helps facilitate clean and simple
algorithm writing and use. It is strongly recommended that
you gain familiarity with these classes before using this
part of the library.
</para><para>
At present, the issue of complex numbers in signal
processing is somewhat fudged, in that a vector of complex
numbers is represented by a vector of real parts and a
vector of imaginary parts, rather than as a single vector
of complex numbers.
</listitem>
</varlistentry>
</variablelist>
</sect2>
<sect2><title>Common Processing model</title>
<para>
In speech, a large number of algorithms follow the same basic
model, in which a waveform is analysed by an algorithm and a
Track, containing a series of time aligned vectors is
produced. Regardless of the type of signal processing, the
basic model is as follows:
<procedure>
<step>
<para> Start with a waveform and a series of analysis
positions, which can be a fixed distance apart of
specified by some other means.
</para></step>
<step><para>
For each analysis position, define a small portion of the
waveform around that position, Multiply this by a
windowing function to produce a vector of speech samples.
</para></step>
<step><para> Pass this to a frame based signal processing
routine which
in outputs values in another vector.
</para> </step>
<step><para> Add this vector to a position in an EST_Track
which correponds to the analysis time position.
</para></step>
</procedure>
Given this model, the signal processing library breaks down into a
number of different types of function:
<variablelist>
<varlistentry>
<term>Utterance based functions </term>
<listitem><para>
Functions which operate on an entire waveform or
track. These break down into:
<variablelist>
<varlistentry>
<term>Analysis Functions
</term>
<listitem>
<para>
which take a waveform and produce a track
</para>
</listitem>
</varlistentry>
<varlistentry>
<term>Synthesis Functions
</term>
<listitem>
<para>
which take a track and produce a waveform
</para>
</listitem>
</varlistentry>
<varlistentry><term>Filter Functions</term>
<listitem>
<para>
which take a waveform and produce a waveform
</para>
</listitem>
</varlistentry>
<varlistentry><term>Conversion Functions</term>
<listitem><para>
which take a track and produce a track
</para></listitem></varlistentry>
</variablelist>
<varlistentry>
<term>Frames based functions</term>
<listitem><para>
Functions which operate on a single frame of speech or
vector coefficients.</para></listitem></varlistentry>
<varlistentry>
<term>Windowing functions</term>
<listitem><para>
which create a windowed frame of speech from a portion
of a waveform.</para></listitem></varlistentry>
</variablelist>
</para>
<para>
Nearly all functions in the signal processing library belong to
one of the above listed types. Quite often functions are
presented on both the utterance and frame level. For example,
there is a function called <function>sig2lpc</function> which
takes a single frame of windowed speech and produces a set of
linear prediction coefficients. There is also a function called
<function><link linkend="sig2coef">sig2coef</link></function> which performs linear prediction
on a whole waveforn, returning the answer in a
Track. <function><link linkend="sig2coef">sig2coef</link></function> uses the common processing
model, and calls <function><link linkend="sig2lpc-1">sig2lpc</link></function> as the algorithm
in the loop.
</para><para>
Partly for historical reasons some functions,
e.g. <function><link linkend="pda">pda</link></function> are only available in the
utterance based form.
</para><para>
When writing signal processing code for this library, it is
often the case that all that needs to be written is the frame
based algorithm, as other algorithms can do the frame shifting
and windowing operations.
</para></sect2>
<sect2><title>Track Allocation, Frames, Channels and
sub-tracks</title>
<para>
The signal processing library makes extensive use of the
advanced features of the track class, specifically the ability
to access single frames and channels.
</para><para>
Given a standard multi-channel track, it is possible to make
a FVector point to any single frame or channel - this is done
by an internal pointer mechanism in EST_FVector. Furthermore,
a track can be made to point to a selected number of channels
or frames in a main track.
</para>
<para>
For example, imagine we have a function that calculates the
covariance matrix for a multi-dimensional track of data. But
the data we actually have contains energy, cepstra and delta
cepstra. It is non-sensical to calculate convariance on
all of this, we just want the cepstra. To do this we use the
sub-track facility to set a temporary track to just the
cepstral coefficients and pass this into the covariance
function. The temporary track has smart pointers into the
original track and hence no data is copied.
</para><para>
Without this facility, either you would have to do a copy
(expensive) or else tell the covariance function which part of
the track to use (hacky).
Extensive documentation describing this process is found in
<xref linkend="sigpr-example-frames">,
<xref linkend="tr-example-sub-tracks"> and
<xref linkend="tr-example-frames-and-channels">.
</para>
</sect2>
</sect1>
<sect1><title>Functions</title>
<toc depth=4></toc>
<sect2><title>Functions for Generating Frames</title>
<para>
The following set of functions perform either a signal
processing operation on a single frame of speech to produce a set of
coefficients, or a transformation on an existing set of coefficients
to produce a new set. In most cases, the first argument to the
function is the input, and the second is the output. It is assumed
that any input speech frame has already been windowed with an
appropriate windowing function (eg. Hamming) - see
\Ref{Windowing mechanisms} on how to produce such a frame. See also
<xref linkend="sigpr-track-func">.
</para><para>
It is also assumed that the output vector is of the correct size. No
resizing is done in these functions as the incoming vectors may be
subvectors of whole tracks etc. In many cases (eg. lpc analysis), an
{\bf order} parameter is required. This is usually derived from the size
of the input or output vectors, and hence is not passed explicitly.
</para>
&docpp-LinearPredictionfunctions-3;
&docpp-Energyandpowerframefunctions-3;
&docpp-FastFourierTransformfunctions-3;
&docpp-Framebasedfilterbankandcepstralanalysis-3;
<sect2><title id="sigpr-track-func">Functions for Generating Tracks</title>
<para>
Functions which operate on a whole waveform and generate coefficients
for a track.
</para>
&docpp-Functionsforusewithframebasedprocessing-3;
&docpp-DeltaandAccelerationcoefficents-3;
&docpp-PitchF0DetectionAlgorithmfunctions-3;
&docpp-PitchmarkingFunctions-3;
&docpp-Spectrogramgeneration-3;
</sect2>
<sect2><title>Functions for Windowing Frames of Waveforms</title>
&docpp-EST-Window-2;
</sect2>
<sect2><title>Filter funtions</title>
<para>
A filter modifies a waveform by changing its frequency
characteristics. The following types of filter are currently
supported:
<variablelist>
<varlistentry><term>FIR filters</term><listitem><para>FIR filters are
general purpose finite impulse response filters which are useful for
band-pass, low-pass and high-pass
filtering. </para></listitem></varlistentry>
<varlistentry><term>Linear Prediction filters</term><listitem><para>
are used to produce LP residuals from waveforms and vice
versa</para></listitem></varlistentry>
<varlistentry><term>Pre Emphasis filters</term><listitem><para> are
simple filters for changing the spectral tilt of a
signal</para></listitem></varlistentry>
<varlistentry><term>Non linear
filters</term><listitem><para>Miscelaneous
filters</para></listitem></varlistentry>
</variablelist>
</para>
&docpp-FIRfilters-3;
&docpp-LinearPredictionfilters-3;
&docpp-PrePostEmphasisfilters--3;
&docpp-Miscelaneousfilters--3;
</sect2>
&docpp-FilterDesign-2;
</sect1>
&sigprexamplesection;
<sect1><title>Programs</title>
<para>The following are exectutable programs which are used for signal
processing:
</para>
<simplesect><title><link
linkend="sigfv-manual">sig2fv</link></title><para> is used to provide
produce a variety of feature vectors given a
waveform.</para></simplesect>
<simplesect><title><link
linkend="spectgen-manual">spectgen</link></title><para> is used to
produce spectrograms from utterances.</para></simplesect>
<simplesect><title><link linkend="sigfilter-manual">sigfilter</link></title><para> performs filtering
operations on waveforms.</para></simplesect>
<simplesect><title><link linkend="pda-manual">pda</link></title><para>
performs pitch detection on waveforms. While sig2fv can perform pitch
detection also, pda offers more control over the operation.
</para></simplesect>
<simplesect><title><link linkend="pitchmark-manual">pitchmark</link><para>produces a set of pitchmarks,
specifying the instant of glottal close from laryngograph waveforms.
</para></simplesect>
<para>The following programs are also useful in signal processing:
</para>
<simplesect><title><link linkend="ch-wave-manual">ch_wave</link></title><para>performs basic operates on
waveforms, such as adding headers, resampling, rescaling, multi to
single channel conversion etc.
</para></simplesect>
<simplesect><title><link linkend="ch-track-manual">ch_track</link></title><para>performs basic operates on
coefficient tracks, such as adding headers, resampling, rescaling,
multi to single channel conversion etc. </para></simplesect>
</sect1>
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&sigfiltermanualsection;
&pdamanualsection;
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