Program to demostrate the convolution theorm in matlab?

Answer 1

To demonstrate the convolution theorem in MATLAB, you can use the following example code. First, define two signals, such as x = [1, 2, 3] and h = [0.5, 1]. Compute their convolution using the conv function, and then verify the theorem by transforming both signals into the frequency domain using the Fast Fourier Transform (FFT), multiplying the results, and then applying the inverse FFT. Here's a simple implementation:

x = [1, 2, 3];
h = [0.5, 1];
conv_result = conv(x, h); % Convolution in time domain

% Frequency domain approach
X = fft(x);
H = fft(h, length(x) + length(h) - 1); % Zero-padding for proper multiplication
Y = X .* H; % Multiply in frequency domain
freq_conv_result = ifft(Y); % Inverse FFT to get back to time domain
disp([conv_result; freq_conv_result']); % Display results

This code illustrates that the convolution of the two signals in the time domain equals the inverse FFT of their product in the frequency domain.