Hi Raeesaha,
As per my understanding, you would like to do the modelling of a sound control system with a speech signal 'track.wav'. Make sure you have the file in your working directory.
Here is a functional code snippet that you might find useful:
% Load the speech signal
[speechSignal, fs] = audioread('track.wav');
% Define the time vector for the given sampling rate
t = 0:1/fs:(length(speechSignal)-1)/fs;
% Define the given function f(t)
f_t = cos(200*pi*t) + 3*sin(500*pi*t);
% Plot the signal in time domain
figure;
subplot(2,1,1);
plot(t, speechSignal);
title('Speech Signal in Time Domain');
xlabel('Time (s)');
ylabel('Amplitude');
subplot(2,1,2);
plot(t, f_t);
title('f(t) = Cos(200*pi*t) + 3*Sin(500*pi*t)');
xlabel('Time (s)');
ylabel('Amplitude');
% Compute the Discrete Fourier Transform (DFT) for 10 seconds
n10 = fs * 10; % Number of samples for 10 seconds
f_speech10 = fft(speechSignal(1:n10));
f_f_t10 = fft(f_t(1:n10));
% Compute the Discrete Fourier Transform (DFT) for 30 seconds
n30 = fs * 30; % Number of samples for 30 seconds
f_speech30 = fft(speechSignal(1:n30));
f_f_t30 = fft(f_t(1:n30));
% Frequency vector for plotting
f10 = (0:n10-1)*(fs/n10);
f30 = (0:n30-1)*(fs/n30);
% Plot the magnitude of the DFT for 10 seconds
figure;
subplot(2,1,1);
plot(f10, abs(f_speech10));
title('Magnitude of DFT of Speech Signal (10 seconds)');
xlabel('Frequency (Hz)');
ylabel('Magnitude');
subplot(2,1,2);
plot(f10, abs(f_f_t10));
title('Magnitude of DFT of f(t) (10 seconds)');
xlabel('Frequency (Hz)');
ylabel('Magnitude');
% Plot the magnitude of the DFT for 30 seconds
figure;
subplot(2,1,1);
plot(f30, abs(f_speech30));
title('Magnitude of DFT of Speech Signal (30 seconds)');
xlabel('Frequency (Hz)');
ylabel('Magnitude');
subplot(2,1,2);
plot(f30, abs(f_f_t30));
title('Magnitude of DFT of f(t) (30 seconds)');
xlabel('Frequency (Hz)');
ylabel('Magnitude');
% Comment on the differences
% When comparing the DFT plots for 10 seconds and 30 seconds, you will notice that the
% frequency resolution improves with the longer sampling duration. This is because the
% frequency resolution is inversely proportional to the duration of the signal. Hence,
% the 30-second DFT plot will show more precise frequency components compared to the
% 10-second DFT plot.
% Compute the spectrogram to analyze the frequency of the signal with respect to time
figure;
spectrogram(speechSignal, 256, [], [], fs, 'yaxis');
title('Spectrogram of Speech Signal');
xlabel('Time (s)');
ylabel('Frequency (Hz)');
figure;
spectrogram(f_t, 256, [], [], fs, 'yaxis');
title('Spectrogram of f(t)');
xlabel('Time (s)');
ylabel('Frequency (Hz)');
Kindly have a look at the following documentation links to have more information on:
- fft function: https://www.mathworks.com/help/matlab/ref/fft.html
- spectrogram: https://www.mathworks.com/help/signal/ref/spectrogram.html
Hope that helps!
Balavignesh
