Verification of the Convolution Theorem

In this program, I used MATLAB to verify the convolution theorem, a fundamental principle stating that convolution operations in the time domain are equivalent to multiplication operations in the frequency domain. The implementation involves generating sample signals, performing direct time-domain convolution using MATLAB's conv() function, and comparing the results with frequency-domain multiplication through Fast Fourier Transform (FFT) operations. Key steps include: applying fft() to convert signals to the frequency domain, performing element-wise multiplication of the spectra, and using ifft() to transform the result back to the time domain. The program incorporates validation checks by comparing the time-domain convolution results with the inverse FFT of the frequency-domain product, calculating the maximum absolute error between the two methods. Detailed comments explain each computational stage, including zero-padding considerations for linear convolution and normalization requirements for FFT operations. This yields an efficient educational tool suitable for demonstrating signal processing concepts or practical applications in spectral analysis.