adding resource code references to work from, playing

.gitignore

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 *~
 *#
 *.pdf
+samples
+*.asv

examples scripts/lpss_fft_example.m

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+close all;
+clear all;
+
+% PARAMS
+Fs = 1000;            % Sampling frequency                    
+T = 1/Fs;             % Sampling period       
+L = 1500;             % Length of signal
+t = (0:L-1)*T;        % Time vector
+
+% SIGNAL
+S = 0.7*sin(2*pi*50*t) + sin(2*pi*120*t);
+
+% FINAL SIGNAL
+%X = S + 2*randn(size(t));
+X = S;
+
+% PLOT TIME DOMAIN
+figure(1)
+plot(1000*t(1:50),X(1:50))
+title('Signal Corrupted with Zero-Mean Random Noise')
+xlabel('t (milliseconds)')
+ylabel('X(t)')
+
+% CALCULATE FFT
+Y = fft(X);
+
+P2 = abs(Y/L);
+P1 = P2(1:L/2+1);
+P1(2:end-1) = 2*P1(2:end-1);
+
+f = Fs*(0:(L/2))/L;
+
+% PLOT FREQ DOMAIN
+figure(2)
+plot(f,P1) 
+title('Single-Sided Amplitude Spectrum of X(t)')
+xlabel('f (Hz)')
+ylabel('|P1(f)|')

examples scripts/lpss_filter_example.m

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+close all;
+clear all;
+
+% b, a, x, (zi, dim)
+% [y, zf] 
+
+% numerator = b
+% demonitator = a
+% signal = x
+
+% initial conditions = zi
+% dimension = dim
+
+% final conditions = zf
+
+% normalises a vector so a(1) is 1

examples scripts/lpss_lpc_example.m

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+close all;
+clear all;
+
+% GENERATE SIGNAl
+noise = randn(50000,1);
+x = filter(1,[1 1/2 1/3 1/4], noise); % 3rd order forward predictor
+x = x(end-4096+1:end); % last 4096 samples of AR process to avoid startup transients
+
+% LPC
+a = lpc(x,3); % signal, filter order
+est_x = filter([0 -a(2:end)],1,x);
+
+% COMPARE LAST 100 SAMPLES OF EACH
+plot(1:100, x(end-100+1:end), 1:100,est_x(end-100+1:end), '--')
+grid
+xlabel('Sample Number')
+ylabel('Amplitude')
+legend('Original signal','LPC estimate')
+
+% PREDICTION ERROR
+e = x - est_x;
+[acs, lags] = xcorr(e,'coeff');
+
+% PLOT AUTOCORRELATION
+figure(2)
+plot(lags, acs)
+grid
+xlabel('Lags')
+ylabel('Normalized Autocorrelation')
+ylim([-0.1 1.1])

lpss_autocorr.m

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+%% lpss_autocorr.m
+%%
+%% Load wav and run through autocorr from econometrics toolbox
+%% Used max range of m lags calculated from sample frequency
+
+close all;
+clear all;
+
+[y, Fs] = audioread('samples/hood_m.wav');
+sample_size = size(y);
+L = sample_size(1); % number of samples
+
+f0 = 60; % low-pitched male speech
+%f0 = 600; % children
+
+m = Fs / f0; % from lecture 2, max number of lags required to search
+
+autocorr(y,'NumLags', m)

lpss_fft.m

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+%% lpss_fft.m
+%%
+%% Load wav and plot in frequency domain using fft
+%% Construct proper one-sided function for display
+
+close all;
+clear all;
+
+[y, Fs] = audioread('samples/hood_m.wav');
+sample_size = size(y);
+L = sample_size(1); % number of samples
+
+% PLOT TIME DOMAIN
+figure(1);
+title('time domain')
+plot(y);
+xlabel('t (milliseconds)');
+ylabel('X(t)');
+
+% CALCULATE FFT
+Y = fft(y);
+P2 = abs(Y/L); % two-sided spectrum
+P1 = P2(1:L/2+1); % single-sided spectrum
+P1(2:end-1) = 2*P1(2:end-1);
+f = Fs*(0:(L/2))/L;
+
+% PLOT FFT
+figure(2);
+title('fft')
+plot(f, P1);
+xlabel('f (Hz)')
+ylabel('|P1(f)|')

lpss_lpc.m

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+%% lpss_lpc.m
+%%
+%% Load wav and calculate LPC coeffs
+
+close all;
+clear all;
+
+ORDER = 40;
+DISPLAY_SAMPLES = 1000;
+
+% READ SIGNAL
+[y, Fs] = audioread('samples/hood_m.wav');
+sample_size = size(y);
+L = sample_size(1); % number of samples
+DISPLAY_SAMPLES = min([DISPLAY_SAMPLES L]);
+
+for ITER=1:ORDER
+    
+    % LPC
+    a = lpc(y,ITER); % signal, filter order
+    est_y = filter(0.02, a, y);
+
+    % PREDICTION ERROR
+    e = y - est_y;
+    [acs, lags] = xcorr(e,'coeff');
+
+    % COMPARE TWO SIGNALS
+    x = 1:DISPLAY_SAMPLES;
+    figure(2)
+    plot(x, y(end-DISPLAY_SAMPLES+1:end), x, est_y(end-DISPLAY_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')
+    legend('Original signal','LPC estimate')
+
+    % PLOT AUTOCORRELATION
+%     figure(2)
+%     plot(lags, acs)
+%     grid
+%     xlabel('Lags')
+%     ylabel('Normalized Autocorrelation')
+%     ylim([-0.1 1.1])
+
+end

lpss_play.m

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+%% lpss_play.m
+%%
+%% Load wav and play
+
+close all;
+clear all;
+
+[y, Fs] = audioread('samples/ee.wav');
+size(y)
+sound(y, Fs)

lpss_spectrogram.m

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+%% lpss_spectrogram.m
+%%
+%% Load wav and plot spectrogram
+
+close all;
+clear all;
+
+WINDOW_NUMBER = 20;
+
+% matrix by audio channel and sample frequency
+[y, Fs] = audioread('samples/hood_m.wav');
+sample_size = size(y);
+window_size = round(sample_size(1) / ((WINDOW_NUMBER + 1)/2));
+
+freqRes = Fs / window_size
+timeRes = window_size / Fs
+
+spectrogram(y, window_size, round(window_size/2), [], Fs, 'yaxis');
+%view(-45, 65) % For spinning the map on its axis for a 3D view
+%colormap bone % grayscale

lpss_spectrogram_iter.m

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+%% lpss_spectrogram_iter.m
+%%
+%% Load wav and plot spectrogram for iterating window sizes
+
+close all;
+clear all;
+
+%WINDOW_NUMBER = 20;
+
+% matrix by audio channel and sample frequency
+[y, Fs] = audioread('samples/hood_m.wav');
+sample_size = size(y);
+
+for WINDOW_NUMBER=1:50
+
+    window_size = round(sample_size(1) / ((WINDOW_NUMBER + 1)/2));
+
+    freqRes = Fs / window_size;
+    timeRes = window_size / Fs;
+
+    spectrogram(y, window_size, round(window_size/2), [], Fs, 'yaxis');
+    %view(-45, 65) % For spinning the map on its axis for a 3D view
+    %colormap bone % grayscale
+    
+    pause(0.05);
+
+end