Functions

sig2lpc()

Produce the full set of linear prediction coefficients from a frame of speech waveform.

Parameters
sig	the frame of input waveform
acf	the autocorrelation coefficients
ref	the reflection coefficients
lpc	the LPC coefficients The order of the lpc analysis is given as the size of the <parameter> lpc <parameter> vector - 1. The coefficients are placed in the locations 1 - size, and the energy is placed in location 0.

lpc2cep()

Calulate cepstral coefficients from lpc coefficients.

It is possible to calculate a set of cepstral coefficients from lpc coefficients using the relationship:

The order of the cepstral analysis can be different from the lpc order. If the cepstral order is greater, interpolation is used (FINISH add equation). Both orders are taken from the lengths of the respective vectors. Note that these cepstral coefficients take on the assumptions (and errors) of the lpc model and hence will not be the same as cepstral coefficients calculated using DFT functions.

Parameters
lpc	the LPC coefficients (input)
lpc	the cepstral coefficients (output)

sig2lpc()

Produce a set linear prediction coefficients from a frame of speech waveform. {\tt sig} is the frame of input waveform, and {\tt lpc} are the LPC coefficients. The {\bf order} of the lpc analysis is given as the size of the {\tt lpc} vector -1. The coefficients are placed in the locations 1 - size, and the energy is placed in location 0.

sig2ref()

Produce a set of reflection coefficients from a frame of speech waveform. {\tt sig} is the frame of input waveform, and {\tt ref} are the LPC coefficients. The {\bf order} of the lpc analysis is given as the size of the {\tt lpc} vector -1. The coefficients are placed in the locations 1 - size, and the energy is placed in location 0.

lpc2ref()

Calculate the reflection coefficients from the lpc coefficients. Note that in the standard linear prediction analysis, the reflection coefficients are generated as a by-product. @see sig2lpc

ref2lpc()

Calculate the linear prediction coefficients from the reflection coefficients. Use the equation:

lpc2lsf()

Calculate line spectral frequencies from linear prediction coefficients. Use the equation:

lsf2lpc()

Calculate line spectral frequencies from linear prediction coefficients. Use the equation:

sig2pow()

Calculate the power for a frame of speech. This is defined as

sig2rms()

Calculate the root mean square energy for a frame of speech. This is defined as

slowFFT()

Basic in-place FFT.

There's no point actually using this - use \Ref{fastFFT} instead. However, the code in this function closely matches the classic FORTRAN version given in many text books, so is at least easy to follow for new users.

The length of real and imag must be the same, and must be a power of 2 (e.g. 128).

FFT()

Alternate name for slowFFT

slowIFFT()

Basic inverse in-place FFT int slowFFT

IFFT()

Alternate name for slowIFFT

power_spectrum()

Power spectrum using the fastFFT function. The power spectrum is simply the squared magnitude of the FFT. The result real and imaginary parts are both set equal to the power spectrum (you only need one of them !)

power_spectrum_slow()

Power spectrum using the slowFFT function

fastFFT()

Fast FFT An optimised implementation by Tony Robinson to be used in preference to slowFFT

sig2fbank()

Calculate the (log) energy (or power) in each channel of a Mel scale filter bank for a frame of speech. The filters are triangular, are evenly spaced and are all of equal width, on a Mel scale. The upper and lower cutoffs of each filter are at the centre frequencies of the adjacent filters. The Mel scale is described under {\tt Hz2Mel}.

sig2fft()

Calculate the energy (or power) spectrum of a frame of speech. The FFT order is determined by the number of samples in the frame of speech, and is a power of 2. Note that the FFT vector returned corresponds to frequencies from 0 to half the sample rate. Energy is the magnitude of the FFT; power is the squared magnitude.

fft2fbank()

Given a Mel filter bank description, bin the FFT coefficients to compute the output of the filters. The first and last elements of {\tt mel_fbank_frequencies} define the lower and upper bound of the first and last filters respectively and the intervening elements give the filter centre frequencies. That is, {\tt mel_fbank_frequencies} has two more elements than {\tt fbank_vec}.

fbank2melcep()

Compute the dicrete cosine transform of log Mel-scale filter bank output to get the Mel cepstral coeffecients for a frame of speech. Optional liftering (filtering in the cepstral domain) can be applied to normalise the magnitudes of the coefficients. This is useful because, typically, the higher order cepstral coefficients are significantly smaller than the lower ones and it is often desirable to normalise the means and variances across coefficients.

The lifter (cepstral filter) used is:

A typical value of L used in speech recognition is 22. A value of L=0 is taken to mean no liftering. This is equivalent to L=1.

make_mel_triangular_filter()

Make a triangular Mel scale filter. The filter is centred at {\tt this_mel_centre} and extends from {\tt this_mel_low} to {\tt this_mel_high}. {\tt half_fft_order} is the length of a power/energy spectrum covering 0Hz to half the sampling frequency with a resolution of {\tt Hz_per_fft_coeff}.

The routine returns a vector of weights to be applied to the energy/power spectrum starting at element {\tt fft_index_start}. The number of points (FFT coefficients) covered by the filter is given by the length of the returned vector {\tt filter}.

sig2coef()

Produce a single set of coefficents from a waveform. The type of coefficient required is given in the argument type. Possible types are:

lpc	linear predictive coding
cep	cepstrum coding from lpc coefficients
melcep	Mel scale cepstrum coding via fbank
fbank	Mel scale log filterbank analysis
lsf	line spectral frequencies
ref	Linear prediction reflection coefficients
power
f0	srpd algorithm
energy	root mean square energy

The order of the analysis is calculated from the number of channels in fv. The positions of the analysis windows must be given by filling in the track's time array.

This function windows the waveform at the intervals given by the track time array. The length of each window is factorthe local time shift. The windowing function is giveb by wf.

Parameters
sig	input waveform
fv	output coefficients. These have been pre-allocated and the number of channels in a indicates the order of the analysis.
type	the types of coefficients to be produced. "lpc", "cep" etc
factor	the frame length factor, i.e. the analysis frame length will be this times the local pitch period.
wf	function for windowing. See \Ref{Windowing mechanisms}

sigpr_base()

Produce multiple coefficients from a waveform by repeated calls to sig2coef.

Parameters
sig	input waveform
fv	output coefficients. These have been pre-allocated and the number of channels in a indicates the order of the analysis.
op	Features structure containing options for analysis order, frame shift etc.
slist	list of types of coefficients required, from the set of possible types that sig2coef can take.

power()

Calculate the power for each frame of the waveform.

Parameters
sig	input waveform
a	output power track
factor	the frame length factor, i.e. the analysis frame length will be this times the local pitch period.

energy()

Calculate the rms energy for each frame of the waveform.

This function calls \Ref{sig2energy}

Parameters
sig	input waveform
a	output coefficients
factor	optional: the frame length factor, i.e. the analysis frame length will be this times the local pitch period.

fbank()

Mel scale filter bank analysis. The Mel scale triangular filters are computed via an FFT (see \Ref{fastFFT}). This routine is required for Mel cepstral analysis (see \Ref{melcep}). The analysis of each frame is done by \Ref{sig2fbank}.

A typical filter bank analysis for speech recognition might use log energy outputs from 20 filters.

Parameters
sig	input waveform
fbank	the output. The number of filters is determined from the number size of this track.
factor	the frame length factor, i.e. the analysis frame length will be this times the local pitch period
wf	function for windowing. See \Ref{Windowing mechanisms}
up	whether the filterbank analysis should use power rather than energy.
take_log	whether to take logs of the filter outputs

melcep()

Mel scale cepstral analysis via filter bank analysis. Cepstral parameters are computed for each frame of speech. The analysis requires \Ref{fbank}. The cepstral analysis of the filterbank outputs is performed by \Ref{fbank2melcep}.

A typical Mel cepstral coefficient (MFCC) analysis for speech recognition might use 12 cepstral coefficients computed from a 20 channel filterbank.

Parameters
sig	input: waveform
mfcc_track	the output
factor	the frame length factor, i.e. the analysis frame length will be this times the local pitch period
fbank_order	the number of Mel scale filters used for the analysis
liftering_parameter	for filtering in the cepstral domain See \Ref{fbank2melcep}
wf	function for windowing. See \Ref{Windowing mechanisms}
include_c0	whether the zero'th cepstral coefficient is to be included
up	whether the filterbank analysis should use power rather than energy.

delta()

Produce a set of delta coefficents for a track

The delta function is used to produce a set of coefficients which estimate the rate of change of a set of parameters. The output track d must be setup before hand, i.e. it must have the same number of frames and channels as tr.

Parameters
tr	input track of base coefficients
d	output track of delta coefficients.
regression_length	number of previous frames on which delta estimation is calculated on.

sigpr_delta()

Produce multiple sets of delta coefficents from a waveform.

Calculate specified types of delta coefficients. This function is used when the base types of coefficients haven't been calculated. This function calls sig2coef to calculate the base types from which the deltas are calculated, and hence the requirements governing the setup of fv for sig2coef also hold here.

Parameters
sig	input waveform
fv	output coefficients. These have been pre-allocated and the number of channels in a indicates the order of the analysis.
op	Features structure containing options for analysis order, frame shift etc.
slist	list of types of delta coefficients required.

sigpr_acc()

Produce multiple sets of acceleration coefficents from a waveform

Calculate specified types of acceleration coefficients. This function is used when the base types of coefficient haven't been calculated. This function calls sig2coef to calculate the base types from which the deltas are calculated, and hence the requirements governing the setup of fv for sig2coef also hold here.

Parameters
sig	input waveform
fv	output coefficients. These have been pre-allocated and the number of channels in a indicates the order of the analysis.
op	Features structure containing options for analysis order, frame shift etc.
slist	list of types of acceleration coefficients required. The delta function is used to produce a set of coefficients which estimate the rate of change of a set of parameters.

pda()

Top level pitch (F0) detection algorithm. Returns a track conatining evenly spaced frames of speech, each containing a F0 value for that point.

At present, only the \Rref{srpd} pitch tracker is implemented, so this is always called regardless of what method is set to.

Parameters
sig	input waveform
fz	output f0 contour
op	parameters for pitch tracker
method	pda method to be used.

icda()

Top level intonation contour detection algorithm. Returns a track conatining evenly spaced frames of speech, each containing a F0 for that point. {\tt icda} differs from \Ref{pda} in that the contour is smoothed, and unvoiced portions have interpolated F0 values.

Parameters
sig	input waveform
fz	output f0 contour
speech	Interpolation is controlled by the <tt>speech</tt> track. When a point has a positive value in the speech track, it is a candidate for interpolation.
op	parameters for pitch tracker
method	pda method to be used.

default_pda_options()

Create a set sensible defaults for use in pda and icda

srpd()

Super resolution pitch trackerer.

srpd is a pitch detection algorithm that produces a fundamental frequency contour from a speech waveform. At present only the super resolution pitch detetmination algorithm is implemented. See (Medan, Yair, and Chazan, 1991) and (Bagshaw et al., 1993) for a detailed description of the algorithm.

Frames of data are read in from sig in chronological order such that each frame is shifted in time from its predecessor by pda_frame_shift. Each frame is analysed in turn.

The maximum and minimum signal amplitudes are initially found over the duration of two segments, each of length N_min samples. If the sum of their absolute values is below two times noise_floor, the frame is classified as representing silence and no coefficients are calculated. Otherwise, a cross correlation coefficient is calculated for all n from a period in samples corresponding to min_pitch to a period in samples corresponding to max_pitch, in steps of decimation_factor. In calculating the coefficient only one in decimation_factor samples of the two segments are used. Such down-sampling permits rapid estimates of the coefficients to be calculated over the range N_min <= n <= N_max. This results in a cross-correlation track for the frame being analysed.

Local maxima of the track with a coefficient value above a specified threshold form candidates for the fundamental period. The threshold is adaptive and dependent upon the values v2uv_coeff_thresh, min_v2uv_coef_thresh , and v2uv_coef_thresh_rati_ratio. If the previously analysed frame was classified as unvoiced or silent (which is the initial state) then the threshold is set to v2uv_coef_thresh. Otherwise, the previous frame was classified as being voiced, and the threshold is set equal to [\-r] v2uv_coef_thresh_rati_ratio times the cross-correlation coefficient value at the point of the previous fundamental period in the former coefficients track. This product is not permitted to drop below v2uv_coef_thresh.

If no candidates for the fundamental period are found, the frame is classified as being unvoiced. Otherwise, the candidates are further processed to identify the most likely true pitch period. During this additional processing, a threshold given by anti_doubling_thres is used.

If the peak_tracking flag is set to true, biasing is applied to the cross-correlation track as described in (Bagshaw et al., 1993).

Parameters
sig	input waveform
op	options regarding pitch tracking parameters
op.min_pitch	minimum permitted F0 value
op.max_pitch	maximum permitted F0 value
op.pda_frame_shift	analysis frame shift
op.pda_frame_length	analysis frame length
op.lpf_cutoff	cut off frequency for low pass filtering
op.lpf_order	order of low pass filtering (must be odd)
op.decimation
op.noise_floor
op.min_v2uv_coef_thresh
op.v2uv_coef_thresh_ratio
op.v2uv_coef_thresh
op.anti_doubling_thresh
op.peak_tracking

smooth_phrase()

Smooth selected parts of an f0 contour. Interpolation is controlled by the speech track. When a point has a positive value in the speech track, it is a candidate for interpolation.

smooth_portion()

Smooth all the points in an F0 contour

pitchmark()

Find pitchmarks in Larynograph (lx) signal.

This high level function places a pitchmark on each positive peak in the voiced portions of the lx signal. Pitchmarks are stored in the time component of a EST_Track object and returned. The function works by high and low pass filtering the signal using forward and backward filtering to remove phase shift. The negative going points in the smoothed differentiated signal, corresponding to peaks in the original are then chosen.

Parameters
lx	laryngograph waveform
op	options, mainly for filter control: \begin{itemize} \item {\bf lx_low_frequency} low pass cut off for lx filtering : typical value {\tt 400} \item {\bf lx_low_order} order of low pass lx filter: typical value 19 \item {\bf lx_high_frequency} high pass cut off for lx filtering: typical value 40 \item {\bf lx_high_order} order of high pass lx filter: typical value 19 \item {\bf median_order} order of high pass lx filter: typical value 19 \end{itemize}

pitchmark()

Find pitchmarks in Larynograph (lx) signal. The function is the same as \Ref{pitchmark} but with more explicit control over the parameters.

Parameters
lx	laryngograph waveform
lx_lf	low pass cut off for lx filtering : typical value 400
lx_fo	order of low pass lx filter : typical value 19
lx_hf	high pass cut off for lx filtering : typical value 40
lx_ho	: typical value 19
mo	order of median smoother used to smoother differentiated lx : typical value 19

neg_zero_cross_pick()

Find times where waveform cross zero axis in negative direction.

Parameters
sig	waveform
pm	pitchmark track which stores time positions of negative crossings

pm_fill()

Produce a set of sensible pitchmarks.

Given a set of raw pitchmarks, this function makes sure no pitch period is shorter that {\tt min} seconds and no longer than {\tt max} seconds. Periods that are too short are eliminated. If a peroid is too long, extra pitchmarks are inserted whose period is {\it approxiamtely} {\tt def} seconds in duration. The approximation is to ensure that the pitch period in the interval, D, is constant, and so the actual pitch period is given by

pm_min_check()

Remove pitchmarks which are too close together.

This doesn't work in a particularly sophisticated way, in that it removes a sequence of too close pitchmarks left to right, and doesn't attempt to find which ones in the sequence are actually spurious.

raw_spectrogram()

Compute the power-spectrogram

scale_spectrogram()

Manipulate the spectrogram to

make_window()

Make a Buffer of containing a window function of specified type

make_window()

Make a EST_FVector containing a window function of specified type

creator()

Return the creation function for the given window type.

window_signal()

Window the waveform {\tt sig} starting at point {\tt start} for a duration of {\tt size} samples. The windowing function required is given as a function pointer {\tt *make_window} which has already been created by a function such as \Ref{creator}. The output windowed frame is placed in the buffer {\tt frame} which will have been resized accordingly within the function.

window_signal()

Window the waveform {\tt sig} starting at point {\tt start} for a duration of {\tt size} samples. The windowing function required is given as a function pointer {\tt *make_window} which has already been created by a function such as \Ref{creator}. The output windowed frame is placed in the EST_FVector {\tt frame}. By default, it is assumed that this is already the correct size (i.e. {\tt size} samples long), but if resizing is required the last argument should be set to 1.

window_signal()

Window the waveform {\tt sig} starting at point {\tt start} for a duration of {\tt size} samples. The windowing function required is given as a string: this function will make a temporary window of this type. The output windowed frame is placed in the EST_FVector {\tt frame}. By default, it is assumed that this is already the correct size (i.e. {\tt size} samples long), but if resizing is required the last argument should be set to 1.

window_signal()

Window the waveform {\tt sig} starting at point {\tt start} for a duration of {\tt size} samples. The window shape required is given as an array of floats. The output windowed frame is placed in the EST_FVector {\tt frame}. By default, it is assumed that this is already the correct size (i.e. {\tt size} samples long), but if resizing is required the last argument should be set to 1.

description()

Return the description for a given window type.

options_supported()

Return a paragraph describing the available windows.

options_short()

Return a comma separated list of the available window types.

FIRfilter()

General purpose FIR filter. This function will filter the waveform {\tt sig} with a previously designed filter, given as {\tt numerator}. The filter coefficients can be designed using one of the designed functions, e.g. \Ref{design_FIR_filter}.

FIRfilter()

General purpose FIR filter. This function will filter the waveform {\tt sig} with a previously designed filter, given as {\tt numerator}. The filter coefficients can be designed using one of the designed functions, e.g. \Ref{design_FIR_filter} .

FIR_double_filter()

General purpose FIR double (zero-phase) filter. This function will double filter the waveform {\tt sig} with a previously designed filter, given as {\tt numerator}. The filter coefficients can be designed using one of the designed functions, e.g. \Ref{design_FIR_filter}. Double filtering is performed by filtering the signal normally, resversing the waveform, filtering again and reversing the waveform again. Normal filtering will impose a lag on the signal depending on the order of the filter. By filtering the signal forwards and backwards, the lags cancel each other out and the output signal is in phase with the input signal.

FIRlowpass_filter()

Quick function for one-off low pass filtering. If repeated lowpass filtering is needed, first design the required filter using \Ref{design_lowpass_filter}, and then use \Ref{FIRfilter} to do the actual filtering.

Parameters
in_sig	input waveform, which will be overwritten
freq
order	number of filter coefficients, eg. 99

FIRlowpass_filter()

Quick function for one-off low pass filtering. If repeated lowpass filtering is needed, first design the required filter using \Ref{design_lowpass_filter}, and then use \Ref{FIRfilter} to do the actual filtering.

Parameters
in_sig	input waveform
out_sig	output waveform
freq	cutoff frequency in Hertz
order	number of filter coefficients , e.g. 99

FIRhighpass_filter()

Quick function for one-off high pass filtering. If repeated lowpass filtering is needed, first design the required filter using design_lowpass_filter, and then use FIRfilter to do the actual filtering.

Parameters
in_sig	input waveform, which will be overwritten
freq	cutoff frequency in Hertz
order	number of filter coefficients, eg. 99

FIRhighpass_filter()

Quick function for one-off high pass filtering. If repeated highpass filtering is needed, first design the required filter using design_highpass_filter, and then use FIRfilter to do the actual filtering.

Parameters
in_sig	input waveform
out_sig	output waveform
freq	cutoff frequency in Hertz
order	number of filter coefficients, eg. 99

FIRhighpass_double_filter()

Quick function for one-off double low pass filtering.

Normal low pass filtering (\Ref{FIRlowpass_filter}) introduces a time delay. This function filters the signal twice, first forward and then backwards, which ensures a zero phase lag. Hence the order parameter need only be half what it is for (\Ref{FIRlowpass_filter} to achieve the same effect.

Parameters
in_sig	input waveform, which will be overwritten
freq	cutoff frequency in Hertz
order	number of filter coefficients, eg. 99

FIRhighpass_double_filter()

Quick function for one-off double low pass filtering.

Normal low pass filtering (\Ref{FIRlowpass_filter}) introduces a time delay. This function filters the signal twice, first forward and then backwards, which ensures a zero phase lag. Hence the order parameter need only be half what it is for (\Ref{FIRlowpass_filter} to achieve the same effect.

Parameters
in_sig	input waveform
out_sig	output waveform
freq	cutoff frequency in Hertz
order	number of filter coefficients, eg. 99

FIRlowpass_double_filter()

Quick function for one-off zero phase high pass filtering.

Normal high pass filtering (\Ref{FIRhighpass_filter}) introduces a time delay. This function filters the signal twice, first forward and then backwards, which ensures a zero phase lag. Hence the order parameter need only be half what it is for (\Ref{FIRhighpass_filter} to achieve the same effect.

Parameters
in_sig	input waveform, which will be overwritten
freq	cutoff frequency in Hertz
order	number of filter coefficients, eg. 99

FIRlowpass_double_filter()

Quick function for one-off zero phase high pass filtering.

Normal high pass filtering (\Ref{FIRhighpass_filter}) introduces a time delay. This function filters the signal twice, first forward and then backwards, which ensures a zero phase lag. Hence the order parameter need only be half what it is for (\Ref{FIRhighpass_filter} to achieve the same effect.

Parameters
in_sig	input waveform
out_sig	output waveform
freq	cutoff frequency in Hertz
order	number of filter coefficients, eg. 99

lpc_filter()

Synthesize a signal from a single set of linear prediction coefficients and the residual values.

Parameters
sig	the waveform to be synthesized
a	a single set of LP coefficients
res	the input residual waveform

inv_lpc_filter()

Filter the waveform using a single set of coefficients so as to produce a residual signal.

Parameters
sig	the speech waveform to be filtered
a	a single set of LP coefficients
res	the output residual waveform

lpc_filter_1()

Synthesize a signal from a track of linear prediction coefficients. This function takes a set of LP frames and a residual and produces a synthesized signal.

For each frame, the function picks an end point, which is half-way between the current frame's time position and the next frame's. A start point is defined as being the previous frame's end. Using these two values, a portion of residual is extracted and passed to \Ref{lpc_filter} along with the LP coefficients for that frame. This function writes directly into the signal for the values between start and end;

Parameters
sig	the waveform to be synthesized
lpc	a track of time positioned LP coefficients
res	the input residual waveform

lpc_filter_fast()

Synthesize a signal from a track of linear prediction coefficients. This function takes a set of LP frames and a residual and produces a synthesized signal.

This is functionally equivalent to \Ref{lpc_filter_1} except it resduces the residual by 0.5 before filtering. Importantly it is about three times faster than \Ref{lpc_filter_1} but in doing so uses direct C buffers rather than the neat C++ access function. This function should be regarded as temporary and will be deleted after we restructure the low level classes to give better access.

Parameters
sig	the waveform to be synthesized
lpc	a track of time positioned LP coefficients
res	the input residual waveform

inv_lpc_filter_ola()

Produce a residual from a track of linear prediction coefficients and a signal using an overlap add technique.

For each frame, the function estimates the local pitch period and picks a start point one period before the current time position and an end point one period after it.

A portion of residual corresponding to these times is then produced using \Ref{inv_lpc_filter}. The resultant section of residual is then overlap-added into the main residual wave object.

Parameters
sig	the speech waveform to be filtered
lpc	a track of time positioned LP coefficients
res	the output residual waveform

pre_emphasis()

Pre-emphasis filtering. This performs simple high pass filtering with a one tap filter of value {\tt a}. Normal values of a range between 0.95 and 0.99.

pre_emphasis()

Pre-emphasis filtering. This performs simple high pass filtering with a one tap filter of value {\tt a}. Normal values of a range between 0.95 and 0.99.

post_emphasis()

Post-emphasis filtering. This performs simple low pass filtering with a one tap filter of value a. Normal values of a range between 0.95 and 0.99. The same values of {\tt a} should be used when pre- and post-emphasizing the same signal.

post_emphasis()

Post-emphasis filtering. This performs simple low pass filtering with a one tap filter of value a. Normal values of a range between 0.95 and 0.99. The same values of {\tt a} should be used when pre- and post-emphasizing the same signal.

simple_mean_smooth()

Filters the waveform by means of median smoothing.

This is a sort of low pass filter which aims to remove extreme values. Median smoothing works examining each sample in the wave, taking all the values in a window of size {\tt n} around that sample, sorting them and replacing that sample with the middle ranking sample in the sorted samples.

Parameters
sig	waveform to be filtered
n	size of smoothing window