added diagrams, started writing up results

lpss.m

@@ -5,16 +5,16 @@
 close all;clear all;clc;
 
 SEGMENT_LENGTH = 100; % ms
-SEGMENT_OFFSET = 0; % ms from start
+SEGMENT_OFFSET = 20; % ms from start
 
-LPC_ORDER = 20;
+LPC_ORDER = 25;
 AC_DISP_SAMPLES = 1000; % autocorrelation display samples
 WINDOW_NUMBER = 10; % number of windows for spectrogram
-WINDOW_OVERLAP = 5; % ms
+WINDOW_OVERLAP = 10; % ms
-SYNTH_WINDOW_NUMBER = 100; % number of windows for spectrogram
+SYNTH_WINDOW_NUMBER = 60; % number of windows for spectrogram
-SYNTH_WINDOW_OVERLAP = 10; % ms
+SYNTH_WINDOW_OVERLAP = 20; % ms
 
-PREEMPHASIS_COEFFS = [1 -0.8]; % first order zero coeff for pre-emphasis
+PREEMPHASIS_COEFFS = [1 -0.9]; % first order zero coeff for pre-emphasis
 
 F0 = 60; % low-pitched male speech
 % F0 = 600; % children
@@ -36,8 +36,9 @@ ORIG_LPC_T_COMPARE = false;
 ORIG_SPECTROGRAM = true;
 SYNTH_SPECTROGRAM = true;
 
-SYNTHESISED_SOUND_LENGTH = 500; % ms
+SYNTHESISED_SOUND_LENGTH = 1000; % ms
 
+WRITE = false;
 PLAY = false;
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@@ -128,7 +129,7 @@ if PREEMPHASIS
 
     prefilter_plot = plot(prefilter_freqs, 20*log10(abs(prefilter_vals)), 'g');
     prefilter_plot.Color(4) = 0.8;
-    prefilter_plot.LineWidth = 1;
+    prefilter_plot.LineWidth = 1.5;
 end
 
 %% PLOT
@@ -191,7 +192,7 @@ maxima_plot.MarkerSize = 8;
 maxima_plot.LineWidth = 1.5;
 
 grid
-xlabel('Quefrency')
+xlabel('Quefrency (samples)')
 ylabel('ceps(x[n])')
 xlim([0 L / 2])
 title('Speech Signal Cepstrum')
@@ -202,7 +203,7 @@ end
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 % CEPSTRUM
 if CEPSTRUM_PLOT && length(cep_maxima_times) >= 1    
-    pitch_period = cep_maxima_times(c == max(c));
+    pitch_period = cep_maxima_times(c == max(c))
     fundamental_freq = 1 / (pitch_period / Fs)
 else
     disp('pitch periods not identified')
@@ -216,7 +217,9 @@ if exist('fundamental_freq')
 
     synth_sound = filter(1, a, excitation);
     
+    if WRITE
     audiowrite('out.wav', synth_sound, Fs);
+    end
 end
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

lpss_lpc.m

@@ -15,8 +15,12 @@ DISPLAY_SAMPLES = min([DISPLAY_SAMPLES L]);
 % CALCULATE FFT
 [freq_dom_freqs, freq_dom_vals] = fft_(y, Fs);
 
+index = 1;
+
 for ITER=1:5:ORDER
     
+    subplot(4, 2, index);
+    
     % LPC
     a = lpc(y,ITER); % signal, filter order
     
@@ -24,12 +28,56 @@ for ITER=1:5:ORDER
     [h, filter_freqs] = freqz(1, a, length(freq_dom_freqs), Fs);
     
     figure(1)
-    plot(freq_dom_freqs, 20*log10(freq_dom_vals), 'r', filter_freqs, 20*log10(abs(h)), 'b')
+    %% SIGNAL FFT RESPONSE
+    orig_freq_plot = plot(freq_dom_freqs, 20*log10(abs(freq_dom_vals)), 'black');
+    orig_freq_plot.Color(4) = 0.1;
+    orig_freq_plot.LineWidth = 1;
+    hold on
+    
+    %% LPC FILTER RESPONSE
+    [filter_vals, filter_freqs] = freqz(1, a, length(freq_dom_freqs), Fs);
+    filter_vals_db = 20*log10(abs(filter_vals));
+
+    lpc_freq_plot = plot(filter_freqs, filter_vals_db, 'b');
+    lpc_freq_plot.LineWidth = 2;
+    
+    %% ARYULE FILTER RESPONSE
+    ary = aryule(y, ITER);
+    [filter_vals, filter_freqs] = freqz(1, ary, length(freq_dom_freqs), Fs);
+    filter_vals_db = 20*log10(abs(filter_vals));
+
+    lpc_freq_plot = plot(filter_freqs, filter_vals_db, 'r');
+    lpc_freq_plot.LineWidth = 1;
+    
+    %% ARCOV FILTER RESPONSE
+    arc = arcov(y, ITER);
+    [filter_vals, filter_freqs] = freqz(1, arc, length(freq_dom_freqs), Fs);
+    filter_vals_db = 20*log10(abs(filter_vals));
+
+    lpc_freq_plot = plot(filter_freqs, filter_vals_db, 'g');
+    lpc_freq_plot.LineWidth = 1;
+    
+%     % 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);
+% 
+%     if length(maxima_freqs) ~= 0
+%         maxima_plot = plot(maxima_freqs, maxima_db, 'rx');
+%         maxima_plot.MarkerSize = 12;
+%         maxima_plot.LineWidth = 2;
+%     end
+    
+    % plot(freq_dom_freqs, 20*log10(freq_dom_vals), 'r', filter_freqs, 20*log10(abs(h)), 'b')
     % plot(w/pi, 20*log10(abs(h)))
+    hold off
     grid
     xlabel('Frequency (Hz)')
     ylabel('Magnitude (dB)')
-    legend('Original Signal', 'LPC Filter')
+%     legend('Original Signal', 'LPC Filter', 'Local Maxima')
+    legend('Original Signal', 'LPC Filter', 'Aryule LPC Filter', 'Arcov LPC Filter')
+    title(strcat(['LPC Spectra: Order ' num2str(ITER)]));
 
     % COMPARE TWO SIGNALS TIME DOMAIN
 %     est_y = filter(0.02, a, y);
@@ -43,7 +91,6 @@ for ITER=1:5:ORDER
 %     ylabel('Amplitude')
 %     legend('Original signal','LPC estimate')
 
-
+    index = index + 1;
-    pause(0.5)
 
 end

report/references.bib

@@ -0,0 +1,12 @@
+@article{formant-frequencies,
+	author = {Scherer, Stefan and Lucas, Gale and Gratch, Jonathan and Rizzo, Albert and Morency, Louis-Philippe},
+	doi = {10.1109/TAFFC.2015.2440264},
+	journal = {IEEE Transactions on Affective Computing},
+	month = {01},
+	pages = {1--1},
+	title = {Self-Reported Symptoms of Depression and PTSD Are Associated with Reduced Vowel Space in Screening Interviews},
+	url = {https://www.researchgate.net/publication/279164505_Self-Reported_Symptoms_of_Depression_and_PTSD_Are_Associated_with_Reduced_Vowel_Space_in_Screening_Interviews},
+	volume = {7},
+	year = {2015}
+}
+