Time-domain convolution doesn't match Frequency-domain multiplication in MATLAB

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Tianjia 2023-2-22

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https://ww2.mathworks.cn/matlabcentral/answers/1916615-time-domain-convolution-doesn-t-match-frequency-domain-multiplication-in-matlab

评论： Askic V 2023-2-22

采纳的回答： Matt J

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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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Matt J 2023-2-22

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编辑：Matt J 2023-2-22

Note that conv() implements linear convolution, not circular convolution.

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Tianjia 2023-2-22

I just found out another, easier way. Use cconv(x, hpf, N) and the result is correct! Thank you for reminding me of the circular and linear thing! I've been thinking about this for almost a week.