Time-domain convolution doesn't match Frequency-domain multiplication in MATLAB
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I wonder why these two lines of codes generate very different results:
subplot(1,2,1);
semilogx(abs(X.*HPF));
subplot(1,2,2);
semilogx(abs(fft(conv(ifft(X),ifft(HPF),'same'))));
I mean, regardless of the actual values of X and HPF, spectrum derived from multiplying X and HPF should have the same results as the spectrum derived from convoluting their time-domain impulse responses (which is derived by ifft). But my results show that they are quite different. In my case x is the input signal that have a few sine wave components at different frequencies and HPF is a high-pass filter, but the two expressions should always yield the same results right? I'm confused.
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