working end to end code

func/autocorr.m

@@ -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, round(max_lags), 'coeff');
-% [cep_autocorr, cep_lags] = xcorr(signal, 'coeff');
+[cep_autocorr, cep_lags] = xcorr(signal, 'coeff');
 
 if time
     cep_lags = 1000*cep_lags/Fs; % turn samples into ms

func/get_impulse_train.m

@@ -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

func/spectro.m

@@ -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
 

lpss.m

@@ -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)')
+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
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+if CEPSTRUM_COMPLEX
+    cep = cceps(y);
+else
     cep = rceps(y);
-% cep = cceps(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_LOW_PASS
-if CEPSTRUM_ONE_SIDED
+    c = cep_filt;
-    plot(ceps_t(1:L / 2), cep(1:L / 2))
 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')
-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

lpss_cepstrum.m

@@ -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
+if CEPSTRUM_FFT
     
-c = cceps(y);
 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;

lpss_preemph.m

@@ -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')

lpss_synth.m

@@ -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)

report/report.lyx

@@ -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
+ The task will be considered as two areas of concern, that of modelling
- modelling and synthesis.
+ 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