Pitch Estimation

Pitch estimation is the process of determining the fundamental frequency of a sound signal.

To estimate the pitch of a sound using the Fourier Transform, the first step is to take a short window of the sound signal and apply the Fourier Transform to it. The resulting frequency-domain representation is then analyzed to identify the frequency with the highest amplitude. This frequency is considered to be the fundamental frequency, or pitch, of the sound.

It's important to note that this method is not always accurate and can be affected by various factors such as noise, multiple sources, and non-harmonic sounds. Also, it's sensitive to the window size and windowing function used.

The first step is to divide the given speech signal into 30-40ms blocks of speech frames. The auto correlation sequence of each frame is then found. The pitch period can be computed by finding the time lag corresponds to the second largest peak from the central peak of autocorrelation sequence.

Activity 3.1

Pitch Estimation using Fourier Transform

[y,fs] = audioread("cirk-barabannaya-drob-i-marsh_-silachi.mp3");

y = y(:,1); % Converts to a single channel

dt = 1/fs;

t = 0:dt:(length(y)*dt)-dt;

figure()

plot(t,y);

title('Song Signal');

xlabel('Time (s)');

ylabel('Amplitude');

figure()

sample_array = 1:length(y);

plot(sample_array,y);

window_size = 2 sec

window_time = 0.5;

window_samples = fs*window_time;

n_windows = floor(length(sample_array)/window_samples);

M(n_windows) = struct('cdata',[],'colormap',[]);

h = figure;

h.Visible = 'on';

aviobj = VideoWriter('myMovie_2.avi');

open(aviobj)

pitch_arr = zeros(1,n_windows);

for i=1:n_windows

filtered_samples = (i-1)*window_samples+1 : i*window_samples+1;

filtered_signal = y(filtered_samples);

% Fourier Transform

L = size(filtered_signal,1);

Fn = fs/2;

FTy = fft(filtered_signal)/L;

Fv = linspace(0, 1, fix(L/2)+1)*Fn;

Iv = 1:numel(Fv);

[~,max_index] = max(abs(FTy(Iv,:))*2);

max_frequency = Fv(max_index(1));

pitch_arr(i) = max_frequency;

%figure()

subplot(3,1,1)

plot(sample_array,y);

yl = ylim;

xl = xlim;

xBox = [(i-1)*window_samples+1,i*window_samples+1,i*window_samples+1, (i-1)*window_samples+1];

yBox = [yl(1),yl(1),yl(2),yl(2)];

patch(xBox, yBox, 'black', 'FaceColor', 'black', 'FaceAlpha', 0.5);

xlabel('Samples')

ylabel('Amplitude')

title("Non Overlapping Window")

grid on

subplot(3,1,2)

t_sample = 0:dt:(length(filtered_signal)*dt)-dt;

plot(t_sample,filtered_signal);

xlabel('Time')

ylabel('Amplitude')

title("Amplitude Vartion of Window")

grid on

subplot(3,1,3)

stem(Fv, abs(FTy(Iv,:))*2);

dim = [.7 .7 .3 .3];

annotate_txt = sprintf("Pitch : %6.f Hz",max_frequency);

t = annotation('textbox',dim,'String', ...

annotate_txt,'FitBoxToText','on');

xlabel('Frequency')

ylabel('Amplitude')

title("Frequency Vartion of Window")

grid on

t.Color = "white";

t.BackgroundColor = "black";

drawnow

pause(0.1)

M(i) = getframe;

frame = getframe(gcf);

writeVideo(aviobj,frame);

end

close(aviobj);

Activity 3.2

Pitch Estimation using Correlation

[y,Fs]= audioread('cirk-barabannaya-drob-i-marsh_-silachi.mp3');

y = y(1:10000,1);

max_value = max(abs(y));

y=y/max_value;

t=(1/Fs:1/Fs:(length(y)/Fs))*1000;

subplot(2,1,1);

plot(t,y);

title('A 30 millisecond segment of speech')

xlabel('time in milliseconds');

sum1=0;autocorrelation=0;

for l=0:(length(y)-1)

sum1=0;

for u=1:(length(y)-l)

s=y(u)*y(u+l);

sum1=sum1+s;

end

autocor(l+1)=sum1;

end

kk=(1/Fs:1/Fs:(length(autocor)/Fs))*1000;

subplot(2,1,2);

plot(kk,autocor);

title('Autocorrelation of the 30 millisecond segment of speech')

xlabel('time in milliseconds');

auto=autocor(21:160);

max1=0;

for uu=1:140

if(auto(uu)>max1)

max1=auto(uu);

sample_no=uu;

end

end

pitch_period_To=(20+sample_no)*(1/Fs)

pitch_freq_Fo=1/pitch_period_To

Reference

https://vlab.amrita.edu/index.php?sub=59&brch=164&sim=1012&cnt=2#:~:text=The%20first%20step%20is%20to,central%20peak%20of%20autocorrelation%20sequence.