  <sect1>
	<title>Signal processing example code</title>

    <toc depth='1'></toc>
    <para>
 
    </para>
    <sect2>
      <title>Producing a single type of feature vector for an utterance</title>
      <para>
A number of types of signal processing can be performed by the
sig2coef function. The following code demonstrates a simple
case of calculating the linear prediction (LP) coefficients for
a waveform.
First set the order of the lpc analysis to 16 (this entails 17 actual
coefficients) and then load in the waveform to be analysed.
      </para>
      <programlisting arch='c'>    
    int lpc_order = 16;
    sig.load(DATA "/kdt_001.wav");      </programlisting>
      <para>
Now allocate enrough space in the track to hold the analysis.
The following command resizes fv to have enough frames for
analysis frames at 0.01 intervals up to the end of the waveform,
(sig.end()), and enough channels to store lpc_order + 1 coefficients.
The channels are named so as to take lpc coefficients.
      </para>
      <programlisting arch='c'>    int num_frames;
    num_frames = (int)ceil(sig.end() / 0.01);
    fv.resize(num_frames, lpc_order + 1);      </programlisting>
      <para>
The positions of the frames, corresponding to the middel of their
analysis window also needs to be set. For fixed frame analysis, this
can be done with the fill_time() function: 
      </para>
      <programlisting arch='c'>    fv.fill_time(0.01);      </programlisting>
      <para>
The simplest way to do the actual analysis is as follows, which
will fill the track with the values from the LP analysis using the
default processing controls.
      </para>
      <programlisting arch='c'>    sig2coef(sig, fv, "lpc");      </programlisting>
      <para>
In this style of analysis, default values are used to control the
windowing mechanisms which split the whole signal into frames.
Specifically, each frame is defined to start a certain distance 
before the time interval, and extending the same distance after.
This distance is calculated as a function of the local window
spacing and can be adjusted as follows:
Extending one time period before and one time period after the
current time mark:
      </para>
      <programlisting arch='c'>    sig2coef(sig, fv, "lpc", 2.0);      </programlisting>
      <para>
Extending 1.5 time periods before and  after the
current time mark, etc;
      </para>
      <programlisting arch='c'>    sig2coef(sig, fv, "lpc", 3.0);      </programlisting>
      <para>
The type of windowing function may be changed also as this
can be passed in as an optional argument. First we 
create a window function (This is explained more in \Ref{Windowing}).
      </para>
      <programlisting arch='c'>    EST_WindowFunc *wf =  EST_Window::creator("hamming");      </programlisting>
      <para>
and then pass it in as the last argument
      </para>
      <programlisting arch='c'>    sig2coef(sig, fv, "lpc", 3.0, wf);      </programlisting>
    </sect2>
    <sect2>
      <title>Pitch-Synchronous vs fixed frame analysis.</title>
      <para>
Most of the core signal processing functions operate on individual
frames of speech and are oblivious as to how these frames were
extracted from the original speech. This allows us to take the frames
from anywhere in the signal: specifically, this facilitates two
common forms of analysis:
<formalpara><title>fixed frame</title><para>
The time points are space at even intervals throughout the signal.
</para></formalpara>
<formalpara><title>pitch-synchronous</title><para> 
The time points represent <emphasis>pitchmarks</emphasis>
and correspond to a specific position in each pitch perdiod,
e.g. the instant of glottal closure.</para></formalpara>
<para>
It is a simple matter to fill the time array, but normally 
pitchmarks are read from a file or taken from another signal
processing algorithm (see \Ref{Pitchmark functions.}).
</para>
<para>
There are many ways to fill the time array for fixed frame analysis.
manually:      
      </para>
      <programlisting arch='c'>    int num_frames = 300;
    fv.resize(num_frames, lpc_order + 1);
    shift = 0.01; // <lineannotation>time interval in seconds</lineannotation>

    for (i = 0; i &lt; num_frames; ++i)
	fv.t(i) = shift * (float) i;      </programlisting>
      <para>
or by use of the  member function \Ref{EST_Track::fill_time} 
      </para>
      <programlisting arch='c'>    fv.fill_time(0.01);      </programlisting>
      <para>
Pitch synchronous values can simply be read from pitchmark
files:
      </para>
      <programlisting arch='c'>    fv.load(DATA "/kdt_001.pm");
    make_track(fv, "lpc", lpc_order + 1);      </programlisting>
      <para>
Regardless of how the time points where obtain, the analysis
function call is just the same:
      </para>
      <programlisting arch='c'>    sig2coef(sig, fv, "lpc");      </programlisting>
    </sect2>
    <sect2 id='sigpr-example-naming-channels'>
      <title>Naming Channels</title>
      <para>
Multiple types of feature vector can be stored in the same Track.
Imagine that we want lpc, cepstrum and power
coefficients in that order in a track. This can be achieved by using
the \Ref{sig2coef} function multiple times, or by the wrap
around \Ref{sigpr_base} function.
</para><para>
It is vitally important here to ensure that before passing the
track to the signal processing functions that it has the correct
number of channels and that these are appropriately named. This is
most easily done using the track map facility, explained
in <LINK LINKEND="proan129">Naming Channels</LINK>
</para><para>
For each call, we only us the part of track that is relevant.
The sub_track member function of \Ref{EST_Track} is used to get
this. In the following example, we are assuming here that 
fv has sufficient space for 17
lpc coefficients, 8 cepstrum  coefficients and power and that
they are stored in that order.
      </para>
      <programlisting arch='c'>    int cep_order = 16;
    EST_StrList map;

    map.append("$lpc-0+" Stringtoi(lpc_order));
    map.append("$cepc-0+" Stringtoi(cep_order));
    map.append("power");

    fv.resize(EST_CURRENT, map);      </programlisting>
      <para>
An alternative is to use <function>add_channels_to_map()</function>
which takes a list of coefficient types and makes a map.
The order of each type of processing is extracted from
op. 
      </para>
      <programlisting arch='c'>    EST_StrList coef_types;

    coef_types.append("lpc");
    coef_types.append("cep");
    coef_types.append("power");

    map.clear();

    add_channels_to_map(map, coef_types, op);
    fv.resize(EST_CURRENT, map);      </programlisting>
      <para>
After allocating the right number of frames and channels 
in {\tt fv}, we extract a sub_track, which has all the frames
(i.e. between 0 and EST_ALL) and all the lpc channels
      </para>
      <programlisting arch='c'>    fv.sub_track(part, 0, EST_ALL, 0, "lpc_0", "lpc_N");      </programlisting>
      <para>
now call the signal processing function on this part:
      </para>
      <programlisting arch='c'>    sig2coef(sig, part, "lpc");      </programlisting>
      <para>
We repeat the procedure for the cepstral coefficients, but this
time take the next 8 channels (17-24 inclusive)  and calculate the coefficients:
      </para>
      <programlisting arch='c'>    fv.sub_track(part, 0, EST_ALL, "cep_0", "cep_N");

    sig2coef(sig, part, "cep");      </programlisting>
      <para>
Extract the last channel for power and call the power function:
      </para>
      <programlisting arch='c'>    fv.sub_track(part, 0, EST_ALL, "power", 1);
    power(sig, part, 0.01);      </programlisting>
      <para>
While the above technique is adequate for our needs and is
a useful demonstration of sub_track extraction, the
\Ref{sigpr_base} function is normally easier to use as it does
all the sub track extraction itself. To perform the lpc, cepstrum
and power analysis, we put these names into a StrList and
call \Ref{sigpr_base}.
      </para>
      <programlisting arch='c'>    base_list.clear(); // <lineannotation>empty the list, just in case</lineannotation>
    base_list.append("lpc");
    base_list.append("cep");
    base_list.append("power");

    sigpr_base(sig, fv, op, base_list);      </programlisting>
      <para>
This will call \Ref{sigpr_track} as many times as is necessary. 
      </para>
    </sect2>
    <sect2>
      <title>Producing delta and acceleration coefficients</title>
      <para>
Delta coefficients represent the numerical differentiation of a
track, and acceleration coefficients represent the second
order numerical differentiation.
By convention, delta coefficients have a "_d" suffix and acceleration
coefficicents "_a". If the coefficient is mulit-dimensional, the
numbers go after the "_d" or "_a".
      </para>
      <programlisting arch='c'>    map.append("$cep_d-0+" Stringtoi(cep_order)); // <lineannotation>add deltas</lineannotation>
    map.append("$cep_a-0+" Stringtoi(cep_order)); // <lineannotation>add accs</lineannotation>

    fv.resize(EST_CURRENT, map); // <lineannotation>resize the track.</lineannotation>      </programlisting>
      <para>

Given a EST_Track of coefficients {\tt fv}, the \Ref{delta}
function is used to produce the delta equivalents {\tt
del}. The following uses the track allocated above and
generates a set of cepstral coefficients and then makes their
delta and acc:
      </para>
      <programlisting arch='c'>    EST_Track del, acc;

    fv.sub_track(part, 0, EST_ALL, 0, "cep_0", "cep_N"); // <lineannotation>make subtrack of coefs</lineannotation>
    sig2coef(sig, part, "cep");  // <lineannotation>fill with cepstra</lineannotation>

    // <lineannotation>make subtrack of deltas</lineannotation>
    fv.sub_track(del, 0, EST_ALL, 0, "cep_d_0", "cep_d_N"); 
    delta(part, del);  // <lineannotation>calculate deltas of part, and place answer in del</lineannotation>

    // <lineannotation>make subtrack of accs</lineannotation>
    fv.sub_track(acc, 0, EST_ALL, 0, "cep_a_0", "cep_a_N"); 
    delta(del, acc);  // <lineannotation>calculate deltas of del, and place answer in acc</lineannotation>      </programlisting>
      <para>
It is possible to directly calculate the delta coefficients of
a type of coefficient, even if we don't have the base type.
\Ref{sigpr_delta} will process the waveform, make a temporary
track of the required type "lpc" and calculate the delta of this.
</para><para>
The following makes a set of delta reflection coefficients:
      </para>
      <programlisting arch='c'>    map.append("$ref_d-0+" Stringtoi(lpc_order)); // <lineannotation>add to map </lineannotation>
    fv.resize(EST_CURRENT, map); // <lineannotation>resize the track.</lineannotation>

    sigpr_delta(sig, fv, op, "ref");      </programlisting>
      <para>
an equivalent function exists for acceleration coefficients:
      </para>
      <programlisting arch='c'>    map.append("$lsf_a-0+" Stringtoi(lpc_order)); // <lineannotation>add acc lsf</lineannotation>
    fv.resize(EST_CURRENT, map); // <lineannotation>resize the track.</lineannotation>

    sigpr_acc(sig, fv, op, "ref");      </programlisting>
    </sect2>
    <sect2>
      <title>Windowing</title>
      <para>
The \Ref{EST_Window} class provides a variety of means to
divide speech into frames using windowing mechanisms.
</para><para>
A window function can be created from a window name using the
\Ref{EST_Window::creator} function:
      </para>
      <programlisting arch='c'>    EST_WindowFunc *hamm =  EST_Window::creator("hamming");
    EST_WindowFunc *rect =  EST_Window::creator("rectangular");      </programlisting>
      <para>
This function can then be used to create a EST_TBuffer of 
window values. In the following example the values from a
256 point hamming window are stored in the buffer win_vals:
      </para>
      <programlisting arch='c'>    EST_FVector frame;
    EST_FVector win_vals;

    hamm(256, win_vals);      </programlisting>
      <para>
The make_windoe function also creates a window:
      </para>
      <programlisting arch='c'>    EST_Window::make_window(win_vals, 256, "hamming");      </programlisting>
      <para>
this can then be used to make a frame of speech from the main EST_Wave
sig. The following example extracts speech starting at sample 1000:
      </para>
      <para>
Alternatively, exactly the same operation can be performed in a
single step by passing the window function to the
\Ref{EST_Window::window_signal} function which takes a
\Ref{EST_Wave} and performs windoing on a section of it,
storing the output in the \Ref{EST_FVector} {\tt frame}.
      </para>
      <programlisting arch='c'>    EST_Window::window_signal(sig, hamm, 1000, 256, frame, 1);      </programlisting>
      <para>
The window function need not be expliticly created, the window
signal can work on just the name of the window type:
      </para>
      <programlisting arch='c'>    EST_Window::window_signal(sig, "hamming", 1000, 256, frame, 1);      </programlisting>
    </sect2>
    <sect2 id='sigpr-example-frames'>
      <title>Frame based signal processing</title>
      <para>
The signal processing library provides an extensize set of functions
which operate on a single frame of coefficients.
The following example shows one method of splitting the signal
into frames and calling a signal processing algorithm.
First set up the track for 16 order LP analysis:
      </para>
      <programlisting arch='c'>    map.clear();
    map.append("$lpc-0+16");
    
    fv.resize(EST_CURRENT, map);      </programlisting>
      <para>
In this example, we take the analysis frame length to be 256 samples
long, and the shift in samples is just the shift in seconds times the
sampling frequency.
      </para>
      <programlisting arch='c'>    int s_length = 256;
    int s_shift =  int(shift * float(sig.sample_rate()));
    EST_FVector coefs;      </programlisting>
      <para>
Now we set up a loop which calculates the frames one at a time.
{\tt start} is the start position in samples of each frame.
The \Ref{EST_Window::window_signal} function is called which
makes a \Ref{EST_FVector} frame of the speech via a hamming window. 
Using the \Ref{EST_Track::frame} function, the EST_FVector 
{\tt coefs} is set to frame {\tt k} in the track. It is important
to understand that this operation involves setting an internal
smart pointer in {\tt coefs} to the memory of frame {\tt k}. This
allows the signal processing function \Ref{sig2lpc} to operate
on an input and output \Ref{EST_FVector}, without any copying to or
from the main track. After the \Ref{sig2lpc} call, the kth frame
of {\tt fv} is now filled with the LP coefficients.
      </para>
      <programlisting arch='c'>    for (int k1 = 0; k1 &lt; fv.num_frames(); ++k1)
    {
	int start = (k1 * s_shift) - (s_length/2);
	EST_Window::window_signal(sig, "hamming", start, s_length, frame, 1);

	fv.frame(coefs, k1); 	// <lineannotation>Extract a single frame</lineannotation>
	sig2lpc(frame, coefs); 	// <lineannotation>Pass this to actual algorithm</lineannotation>
    }      </programlisting>
      <para>
A slightly different tack can be taken for pitch-synchronous analysis.
Setting up fv with the pitchmarks and channels:
      </para>
      <programlisting arch='c'>    fv.load(DATA "/kd1_001.pm");
    fv.resize(EST_CURRENT, map);      </programlisting>
      <para>
Set up as before, but this time calculate the window starts and 
lengths from the time points. In this example, the length is a 
{\tt factor} (twice) the local frame shift.
Note that the only difference between this function and the fixed
frame one is in the calculation of the start and end points - the
windowing, frame extraction and call to \Ref{sig2lpc} are exactly
the same.
      </para>
      <programlisting arch='c'>    float factor = 2.0;

    for (int k2 = 0; k2 &lt; fv.num_frames(); ++k2)
    {
	s_length = irint(get_frame_size(fv, k2, sig.sample_rate())* factor);
	int start = (irint(fv.t(k2) * sig.sample_rate()) - (s_length/2));

	EST_Window::window_signal(sig, wf, start, s_length, frame, 1);

	fv.frame(coefs, k2);
	sig2lpc(frame, coefs);
    }      </programlisting>
    </sect2>
    <sect2>
      <title>Filtering </title>
      <para>
In the EST library we so far have two main types of filter,
{\bf finite impulse response (FIR)} filters and {\bf linear
prediction (LP)} filters. {\bf infinite impulse response (IIR)}
filters are not yet implemented, though LP filters are a
special case of these.
</para><para>
Filtering involves 2 stages: the design of the filter and the
use of this filter on the waveform.  
</para><para>
First we examine a simple low-pass filter which attempts to supress
all frequencies about a cut-off. Imagine we want to low pass filter
a signal at 400Hz. First we design the filter:
      </para>
      <programlisting arch='c'>    EST_FVector filter;
    int freq = 400;
    int filter_order = 99;

    filter = design_lowpass_FIR_filter(sig.sample_rate(), 400, 99);      </programlisting>
      <para>
And now use this filter on the signal:
      </para>
      <programlisting arch='c'>    FIRfilter(sig, filter);      </programlisting>
      <para>
For one-off filtering operations, the filter design can be
done in the filter function itself. The \Ref{FIRlowpass_filter}
function takes the signal, cut-off frequency and order as
arguments and designs the filter on the fly. Because of the
overhead of filter design, this function is expensive and
should only be used for one-off operations.
      </para>
      <programlisting arch='c'>    FIRlowpass_filter(sig, 400, 99);      </programlisting>
      <para>
The equivalent operations exist for high-pass filtering:
      </para>
      <programlisting arch='c'>    filter = design_highpass_FIR_filter(sig.sample_rate(), 50, 99);
    FIRfilter(sig, filter);
    FIRhighpass_filter(sig, 50, 99);      </programlisting>
      <para>
Filters of arbitrary frequency response can also be designed using
the \Ref{design_FIR_filter} function. This function takes a
EST_FVector of order $2^{N}$ which specifies the desired frequency
response up to 1/2 the sampling frequency. The function returns
a set of filter coefficients that attempt to match the desired
reponse.
      </para>
      <programlisting arch='c'>    EST_FVector response(16);
    response[0] = 1;
    response[1] = 1;
    response[2] = 1;
    response[3] = 1;
    response[4] = 0;
    response[5] = 0;
    response[6] = 0;
    response[7] = 0;
    response[8] = 1;
    response[9] = 1;
    response[10] = 1;
    response[11] = 1;
    response[12] = 0;
    response[13] = 0;
    response[14] = 0;
    response[15] = 0;

    filter = design_FIR_filter(response, 15);

    FIRfilter(sig, response);      </programlisting>
      <para>
The normal filtering functions can cause a time delay in the
filtered waveform. To attempt to eliminate this, a set of
double filter function functions are provided which guarentess
zero phase differences between the original and filtered waveform.
      </para>
      <programlisting arch='c'>    FIRlowpass_double_filter(sig, 400);
    FIRhighpass_double_filter(sig, 40);      </programlisting>
      <para>
Sometimes it is undesirable to have the input signal overwritten.
For these cases, a set of parallel functions exist which take
a input waveform for reading and a output waveform for writing to.
      </para>
      <programlisting arch='c'>    EST_Wave sig_out;

    FIRfilter(sig, sig_out, response);
    FIRlowpass_filter(sig, sig_out, 400);
    FIRhighpass_filter(sig, sig_out, 40);      </programlisting>
    </sect2>
  </sect1>
