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working end to end code

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aj 2020-11-06 19:08:42 +00:00
parent 438f25c7ca
commit 05dd7680b6
8 changed files with 418 additions and 52 deletions
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4
func/autocorr.m
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@ -1,7 +1,7 @@
function [cep_autocorr, cep_lags] = autocorr(signal, max_lags, time, Fs)
[cep_autocorr, cep_lags] = xcorr(signal, max_lags, 'coeff');
% [cep_autocorr, cep_lags] = xcorr(signal, 'coeff');
% [cep_autocorr, cep_lags] = xcorr(signal, round(max_lags), 'coeff');
[cep_autocorr, cep_lags] = xcorr(signal, 'coeff');
if time
cep_lags = 1000*cep_lags/Fs; % turn samples into ms

27
func/get_impulse_train.m Normal file
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@ -0,0 +1,27 @@
%% get_impulse_train.m
%%
%% Generate periodic impulse train for use in speech synth
%%
%% Signal of pitch fundamental_freq sampled at sampling_freq
%% for time length_ms
function signal = get_impulse_train(fundamental_freq, sampling_freq, length_ms)
if fundamental_freq > sampling_freq
disp('Fundamental frequency greater than sampling_freq')
signal = [];
return
end
required_samples = ms_to_samples(length_ms, sampling_freq);
pitch_period = 1 / fundamental_freq;
sample_period = 1 / sampling_freq;
cell_length = round(pitch_period / sample_period);
% cell to be repeated into periodic signal
pitch_cell = [1 zeros(1, cell_length - 1)];
required_cells = ceil(required_samples / cell_length);
signal = repmat(pitch_cell, 1, required_cells);
signal = signal(1:required_samples);
end

9
func/spectro.m
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@ -2,13 +2,16 @@ function spectro(signal, sample_frequency, windows, overlap_interval)
sample_overlap = ms_to_samples(overlap_interval, sample_frequency);
sample_size = size(signal);
%window_size = round(sample_size(1) / ((windows + 1)/2))
% Turn windows into window width in samples, take into account overlap
window_size = round((sample_size(1) + (windows + 1) * sample_overlap) / (windows+1));
window_size = round(...
(length(signal) + (windows + 1) * sample_overlap) ...
/ ...
(windows+1) ...
);
spectrogram(signal, window_size, sample_overlap, [], sample_frequency, 'yaxis');
spectrogram(signal, window_size, round(sample_overlap), [], sample_frequency, 'yaxis');
end

160
lpss.m
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@ -9,30 +9,52 @@ SEGMENT_OFFSET = 0; % ms from start
LPC_ORDER = 20;
AC_DISP_SAMPLES = 1000; % autocorrelation display samples
WINDOW_NUMBER = 10;
WINDOW_NUMBER = 10; % number of windows for spectrogram
WINDOW_OVERLAP = 5; % ms
SYNTH_WINDOW_NUMBER = 100; % number of windows for spectrogram
SYNTH_WINDOW_OVERLAP = 10; % ms
PREEMPHASIS_COEFFS = [1 -0.8]; % first order zero coeff for pre-emphasis
F0 = 60; % low-pitched male speech
% F0 = 600; % children
% flags for selective running
FREQ_RESPONSE = ~false;
PREEMPHASIS = false;
CEPSTRUM_LOW_PASS = true; % smooth cepstrum for fund. freq. isolation
CEPSTRUM_LOW_PASS_COEFFS = [1 -0.7];
FREQ_RESPONSE = true;
AUTOCORRELATION = false;
CEPSTRUM_PLOT = false;
CEPSTRUM_ONE_SIDED = true;
CEPSTRUM_COMPLEX = false; % else real cepstrum
CEPSTRUM_PLOT = true;
CEPSTRUM_THRESHOLD = 0.075; % threshold for isolating peaks in cepstrum
ORIG_LPC_T_COMPARE = false;
ORIG_SPECTROGRAM = false;
ORIG_SPECTROGRAM = true;
SYNTH_SPECTROGRAM = true;
SYNTHESISED_SOUND_LENGTH = 500; % ms
PLAY = false;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% READ SIGNAL
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
[y, Fs] = audioread('samples/hood_m.wav');
[y, Fs] = audioread('samples/head_f.wav');
% take segment of sample for processing
y = clip_segment(y, Fs, SEGMENT_LENGTH, SEGMENT_OFFSET);
y_orig = y;
L = length(y) % number of samples
if PREEMPHASIS
y = filter(PREEMPHASIS_COEFFS, 1, y);
end
max_lag = Fs/ F0;
L = length(y); % number of samples
max_lag = Fs/ F0; % for autocorrelation
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% LPC
@ -47,12 +69,11 @@ if ORIG_LPC_T_COMPARE
x = 1:AC_DISP_SAMPLES;
AC_DISP_SAMPLES = min([AC_DISP_SAMPLES L]);
% plot t domain for original signal and estimation using LPC coeffs
figure(1)
plot(x, y(end-AC_DISP_SAMPLES+1:end), x, est_y(end-AC_DISP_SAMPLES+1:end), '--')
% plot(x, y(end-DISPLAY_SAMPLES+1:end))
% plot(x, est_y(end-DISPLAY_SAMPLES+1:end))
grid
xlabel('Sample Number')
ylabel('Amplitude')
@ -62,12 +83,12 @@ end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% T DOMAIN PREDICTION ERROR
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
t_domain_err = y - est_y;
t_domain_err = y - est_y; % residual?
if AUTOCORRELATION
figure(2)
[acs, lags] = autocorr(t_domain_err, max_lag, true, Fs);
title('Autocorrelation for error in Time domain')
title('Autocorrelation of error in time domain')
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@ -92,60 +113,114 @@ lpc_freq_plot = plot(filter_freqs, filter_vals_db, 'b');
lpc_freq_plot.LineWidth = 2;
% MAXIMA
% estimate formant frequencies from maxima of LPC filter freq response
maxima = islocalmax(filter_vals_db);
maxima_freqs = filter_freqs(maxima)
maxima_db = filter_vals_db(maxima)
maxima_db = filter_vals_db(maxima);
maxima_plot = plot(maxima_freqs, maxima_db, 'rx');
maxima_plot.MarkerSize = 12;
maxima_plot.LineWidth = 2;
%% PRE_FILTER LPC
if PREEMPHASIS
[prefilter_vals, prefilter_freqs] = freqz(1, lpc(y_orig, LPC_ORDER), length(freq_dom_freqs), Fs);
prefilter_plot = plot(prefilter_freqs, 20*log10(abs(prefilter_vals)), 'g');
prefilter_plot.Color(4) = 0.8;
prefilter_plot.LineWidth = 1;
end
%% PLOT
hold off
grid
xlabel('Frequency (Hz)')
ylabel('Magnitude (dB)')
legend('Original Signal', 'LPC Filter', 'LPC Maxima')
if PREEMPHASIS
legend('Original Signal', 'LPC Filter', 'LPC Maxima', 'LPC No Pre-emphasis')
else
legend('Original Signal', 'LPC Filter', 'LPC Maxima')
end
title('Frequency Response For Speech Signal and LPC Filter')
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% CEPSTRUM
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
cep = rceps(y);
% cep = cceps(y);
if CEPSTRUM_COMPLEX
cep = cceps(y);
else
cep = rceps(y);
end
cep_filt = filter(1, CEPSTRUM_LOW_PASS_COEFFS, cep);
if CEPSTRUM_PLOT
if CEPSTRUM_PLOT % plot cepstrum in t domain
ceps_t = (0:L - 1);
figure(4)
if CEPSTRUM_ONE_SIDED
plot(ceps_t(1:L / 2), cep(1:L / 2))
if CEPSTRUM_LOW_PASS
c = cep_filt;
else
plot(ceps_t(1:L), cep(1:L))
c = cep;
end
figure(4)
hold on
plot(ceps_t(1:round(L / 2)), c(1:round(L / 2)))
%% MAXIMA
% value threshold
c(c < CEPSTRUM_THRESHOLD) = 0;
cep_maxima_indexes = islocalmax(c);
cep_maxima_times = ceps_t(1:round(L / 2));
cep_maxima_times = ceps_t(cep_maxima_indexes);
c = c(cep_maxima_indexes);
% quefrency threshold
cep_time_indexes = 20 < cep_maxima_times;
cep_maxima_times = cep_maxima_times(cep_time_indexes);
c = c(cep_time_indexes);
% 1st half
cep_half_indexes = cep_maxima_times <= round(L / 2);
cep_maxima_times = cep_maxima_times(cep_half_indexes);
c = c(cep_half_indexes);
maxima_plot = plot(cep_maxima_times, c, 'rx');
maxima_plot.MarkerSize = 8;
maxima_plot.LineWidth = 1.5;
grid
xlabel('Quefrency')
ylabel('ceps(x[n])')
if CEPSTRUM_ONE_SIDED
xlim([0 L / 2])
title('One-sided Speech Signal Cepstrum')
else
xlim([0 L])
title('Speech Signal Cepstrum')
end
end
%% AUTOCORRELATION
if AUTOCORRELATION
figure(5)
[cep_autocorr, cep_lags] = autocorr(cep(1:L/2), max_lag, true, Fs);
title('One-sided Cepstrum Autocorrelation')
xlim([0 L / 2])
title('Speech Signal Cepstrum')
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% PLOT ORIGINAL SPECTROGRAM
%% CALCULATE FUNDAMENTAL FREQUENCY
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% CEPSTRUM
if CEPSTRUM_PLOT && length(cep_maxima_times) >= 1
pitch_period = cep_maxima_times(c == max(c));
fundamental_freq = 1 / (pitch_period / Fs)
else
disp('pitch periods not identified')
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% GENERATE SIGNAL
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
if exist('fundamental_freq')
excitation = get_impulse_train(fundamental_freq, Fs, SYNTHESISED_SOUND_LENGTH);
synth_sound = filter(1, a, excitation);
audiowrite('out.wav', synth_sound, Fs);
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% SPECTROGRAM
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
if ORIG_SPECTROGRAM
figure(6)
@ -154,9 +229,20 @@ colormap bone
title('Speech Signal Spectrogram')
end
if SYNTH_SPECTROGRAM
figure(7)
spectro(synth_sound, Fs, SYNTH_WINDOW_NUMBER, SYNTH_WINDOW_OVERLAP);
colormap bone
title('Synthesised Vowel Sound Spectrogram')
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% PLAY
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
if PLAY
sound(y, Fs);
pause(1);
if exist('synth_sound')
sound(synth_sound, Fs);
end
end

55
lpss_cepstrum.m
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@ -5,6 +5,12 @@
close all;clear all;clc;
CEPSTRUM_COEFFS = 100;
CEPSTRUM_THRESHOLD = 0.1;
LOW_PASS_COEFF = 0.9;
F0 = 60; % low-pitched male speech
% F0 = 600; % children
CEPSTRUM_FFT = false;
% READ SIGNAL
[y, Fs] = audioread('samples/hood_m.wav');
@ -21,10 +27,11 @@ xlabel('Quefrency')
ylabel('ceps(x[n])')
% xlim([0 sample_length])
xlim([0 half])
title('Cepstrum')
%% PLOT FFT
c = cceps(y);
if CEPSTRUM_FFT
c(CEPSTRUM_COEFFS:end) = 0;
% [cep_freqs, cep_vals] = fft_(c, Fs);
cep_vals = fft(c);
@ -32,6 +39,46 @@ cep_vals = cep_vals(1:floor(sample_length/2+1));
cep_freqs = Fs*(0:(sample_length/2))/sample_length;
figure(2)
cep_plot = plot(cep_freqs, 20*log10(abs(cep_vals)), 'g');
cep_plot = plot(cep_freqs, 20*log10(abs(cep_vals)));
cep_plot.LineWidth = 2;
hold off
end
%% SMOOTH CEPSTRUM
a = [1 -LOW_PASS_COEFF];
[filter_vals, filter_freqs] = freqz(1, a, 1000, Fs);
figure(3)
plot(filter_freqs, 20*log10(filter_vals));
xlabel('Frequency (Hz)')
ylabel('Amplitude (dB)')
title('Low Pass Filter Response')
c_filt = filter(1, a, c);
figure(4)
plot(t(1:half), c_filt(1:half));
xlabel('Quefrency')
ylabel('ceps(x[n])')
title('Cepstrum Post-Low-Pass')
%% AUTOCORELLATION
figure(5)
autocorr(c(1:half), Fs/F0, true, Fs);
title('Cepstrum Autocorrelation')
figure(6)
[smooth_cep_autocorr, smooth_cep_lags] = autocorr(c_filt(1:half), Fs/F0, true, Fs);
title('Smoothed Cepstrum Autocorrelation')
hold on
smooth_cep_autocorr(smooth_cep_autocorr < CEPSTRUM_THRESHOLD) = 0;
maxima = islocalmax(smooth_cep_autocorr);
maxima_freqs = smooth_cep_lags(maxima)
maxima_db = smooth_cep_autocorr(maxima);
maxima_plot = plot(maxima_freqs, maxima_db, 'rx');
maxima_plot.MarkerSize = 8;
maxima_plot.LineWidth = 1.5;

45
lpss_preemph.m Normal file
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@ -0,0 +1,45 @@
%% lpss_preemph.m
%%
%% Load wav and play with preemphasis filter
close all;clear all;clc;
[y, Fs] = audioread('samples/hood_m.wav');
b = [1 -0.68];
[filter_vals, filter_freqs] = freqz(b, 1, 1000, Fs);
%% PREEMPH FILTER RESPONSE
figure(1)
plot(filter_freqs, filter_vals);
xlabel('Frequency (Hz)')
ylabel('Amplitude')
%% ORIGINAL FFT
[freq_dom_freqs, freq_dom_vals] = fft_(y, Fs);
figure(2)
plot(freq_dom_freqs, 20*log10(freq_dom_vals));
xlabel('Frequency (Hz)')
ylabel('Amplitude')
title('Original spectrum')
%% POST FILTER FFT
y_filt = filter(b, 1, y);
[freq_dom_freqs_post, freq_dom_vals_post] = fft_(y_filt, Fs);
figure(3)
plot(freq_dom_freqs_post, 20*log10(freq_dom_vals_post));
xlabel('Frequency (Hz)')
ylabel('Amplitude')
title('Post-filter spectrum')
%% BOTH
figure(4)
plot(freq_dom_freqs, 20*log10(freq_dom_vals), 'b');
hold on
plot(freq_dom_freqs_post, 20*log10(freq_dom_vals_post), 'r--');
hold off
xlabel('Frequency (Hz)')
ylabel('Amplitude')
legend('Original Signal', 'Filtered')
title('Post-filter spectrum')

11
lpss_synth.m Normal file
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@ -0,0 +1,11 @@
%% lpss.m
%%
%% Coursework script
close all;clear all;clc;
Fs = 24000; % Hz, sampling
Ff = 100; % Hz, fundamental
sample_length = 1000; % ms
sample = get_impulse_train(Ff, Fs, sample_length)

159
report/report.lyx
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@ -268,8 +268,8 @@ Brief
\begin_layout Standard
The aim of this report is to demonstrate how digital signal processing technique
s can be used to analyse, model and synthesise speech.
The task will take will be considered as two areas of concern, that of
modelling and synthesis.
The task will be considered as two areas of concern, that of modelling
and synthesis.
\end_layout
\begin_layout Standard
@ -280,7 +280,7 @@ The modelling stage will utilise Linear Predictive Coding and the source-filter
the original sound will be presented, the effect of different filter orders
will also be demonstrated.
Relevant parameters of the original vowel speech segment will be presented
including the fundamental frequency and further formant frequencies.
including the fundamental frequency and formant frequencies.
\end_layout
\begin_layout Standard
@ -296,10 +296,123 @@ d and analysed.
Implementation
\end_layout
\begin_layout Standard
The implementation of this system was completed using
\noun on
Matlab
\noun default
with aid from functions in the digital signal processing toolbox among
others.
Following loading a vowel sample, a segment of changing length (100ms was
standard) was clipped for processing.
The clip optionally also underwent pre-emphasis using a high pass filter.
As speech spectra can tend to have higher energy at lower frequencies,
the use of pre-emphasis can balance the magnitude across the spectrum.
A first order filter was used and the coefficient varied, over-use could
prove excessive for higher frequencies including fricative sounds.
\end_layout
\begin_layout Subsection
Modelling
\end_layout
\begin_layout Standard
In order to estimate the filter state of the vocal tract, the linear predictive
coding coefficients of varying orders were calculated using the
\begin_inset listings
lstparams "language=Matlab,basicstyle={\ttfamily},tabsize=4"
inline true
status open
\begin_layout Plain Layout
lpc(signal, order)
\end_layout
\end_inset
function.
In order to compare the frequency response of the LPC filter with the original
signal, the Fourier transform of the signal was calculated.
The frequency domain representation of the LPC filter was found using the
\begin_inset listings
lstparams "language=Matlab,basicstyle={\ttfamily},tabsize=4"
inline true
status open
\begin_layout Plain Layout
freqz(b, a, n, f)
\end_layout
\end_inset
function and co-plotted with the original signal.
This frequency plot of the LPC filter constitutes the spectral envelope
of the signal and the vowel formant frequencies can be found at the maxima
of the spectrum.
Due to the smooth profile of the LPC spectrum, formant frequencies were
estimated by identifying the local maxima of the function.
\end_layout
\begin_layout Standard
In order to find the fundamental frequency of the signal, the cepstrum was
used.
The use of a low pass filter was investigated in order to smooth the cepstrum
before programmatically finding pitch period candidates by applying
\begin_inset Formula $x$
\end_inset
and
\begin_inset Formula $y$
\end_inset
thresholds.
\end_layout
\begin_layout Subsection
Synthesis
\end_layout
\begin_layout Standard
In order to synthesise speech, a periodic impulse train at the identified
fundamental frequency of the original vowel was generated.
The impulse train was sampled at the same frequency as the original sound.
\end_layout
\begin_layout Section
Results
\end_layout
\begin_layout Subsection
LPC Filter
\end_layout
\begin_layout Subsubsection
Order Variation
\end_layout
\begin_layout Subsection
Spectral Analysis
\end_layout
\begin_layout Subsubsection
Fundamental Frequency
\end_layout
\begin_layout Subsubsection
Formant Frequencies
\end_layout
\begin_layout Subsubsection
Cepstrum Smoothing
\end_layout
\begin_layout Subsection
Synthesis
\end_layout
\begin_layout Section
Discussion
\end_layout
@ -346,15 +459,38 @@ name "sec:Code"
\end_layout
\begin_layout Standard
While much of the code was developed in individual scripts in order to experimen
t with separate aspects of the system, for collecting results a script which
constitutes the entire system was written,
\begin_inset listings
lstparams "basicstyle={\ttfamily}"
inline true
status open
\begin_layout Plain Layout
lpss.m
\end_layout
\end_inset
.
\end_layout
\begin_layout Standard
\begin_inset CommandInset include
LatexCommand lstinputlisting
filename "../lpss.m"
lstparams "breaklines=true,frame=tb,language=Matlab,basicstyle={\\ttfamily},commentstyle={\\color{commentgreen}\\itshape},keywordstyle={\\color{blue}},emphstyle={\\color{red}},stringstyle={\\color{red}},identifierstyle={\\color{cyan}},morekeywords={audioread, aryule, xcorr, freqz, spectrogram, mfcc, spectro, fft_, autocorr, clip_segment, islocalmax, ms_to_samples},caption={Main script},label={main_script}"
lstparams "breaklines=true,frame=tb,language=Matlab,basicstyle={\\ttfamily},commentstyle={\\color{commentgreen}\\itshape},keywordstyle={\\color{blue}},emphstyle={\\color{red}},stringstyle={\\color{red}},identifierstyle={\\color{cyan}},morekeywords={audioread, aryule, xcorr, freqz, spectrogram, mfcc, spectro, fft_, autocorr, clip_segment, islocalmax, ms_to_samples, rceps, cceps, ones, audioplayer, play, get_impulse_train, lpc},caption={Main script including source-filter model and spectral analysis},label={main_script}"
\end_inset
\begin_inset Newpage pagebreak
\end_inset
\end_layout
\begin_layout Standard
@ -394,7 +530,7 @@ lstparams "breaklines=true,frame=tb,language=Matlab,basicstyle={\\ttfamily},comm
\begin_inset CommandInset include
LatexCommand lstinputlisting
filename "../func/clip_segment.m"
lstparams "breaklines=true,frame=tb,language=Matlab,basicstyle={\\ttfamily},commentstyle={\\color{commentgreen}\\itshape},keywordstyle={\\color{blue}},emphstyle={\\color{red}},stringstyle={\\color{red}},identifierstyle={\\color{cyan}},morekeywords={audioread, aryule, xcorr, freqz, spectrogram},caption={Retrieve a segment of the original speech signal},label={clip_segment_function}"
lstparams "breaklines=true,frame=tb,language=Matlab,basicstyle={\\ttfamily},commentstyle={\\color{commentgreen}\\itshape},keywordstyle={\\color{blue}},emphstyle={\\color{red}},stringstyle={\\color{red}},identifierstyle={\\color{cyan}},morekeywords={audioread, aryule, xcorr, freqz, spectrogram, ms_to_samples},caption={Retrieve a segment of the original speech signal},label={clip_segment_function}"
\end_inset
@ -405,7 +541,18 @@ lstparams "breaklines=true,frame=tb,language=Matlab,basicstyle={\\ttfamily},comm
\begin_inset CommandInset include
LatexCommand lstinputlisting
filename "../func/ms_to_samples.m"
lstparams "breaklines=true,frame=tb,language=Matlab,basicstyle={\\ttfamily},commentstyle={\\color{commentgreen}\\itshape},keywordstyle={\\color{blue}},emphstyle={\\color{red}},stringstyle={\\color{red}},identifierstyle={\\color{cyan}},morekeywords={audioread, aryule, xcorr, freqz, spectrogram},caption={Transform time in milliseconds into the respective number of samples},label={clip_segment_function-1}"
lstparams "breaklines=true,frame=tb,language=Matlab,basicstyle={\\ttfamily},commentstyle={\\color{commentgreen}\\itshape},keywordstyle={\\color{blue}},emphstyle={\\color{red}},stringstyle={\\color{red}},identifierstyle={\\color{cyan}},morekeywords={audioread, aryule, xcorr, freqz, spectrogram},caption={Transform time in milliseconds into the respective number of samples},label={ms_to_samples_function}"
\end_inset
\end_layout
\begin_layout Standard
\begin_inset CommandInset include
LatexCommand lstinputlisting
filename "../func/get_impulse_train.m"
lstparams "breaklines=true,frame=tb,language=Matlab,basicstyle={\\ttfamily},commentstyle={\\color{commentgreen}\\itshape},keywordstyle={\\color{blue}},emphstyle={\\color{red}},stringstyle={\\color{red}},identifierstyle={\\color{cyan}},morekeywords={audioread, aryule, xcorr, freqz, spectrogram, ms_to_samples, repmat},caption={Generate an impulse rate of given fundamental frequency at a provided sampling frequency for a given length of time},label={get_impulse_train_function}"
\end_inset