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This question already has an answer here:

As the question suggest, can anyone explain intuitively why the convolution theorem works ?

For convolution theorem, I refer to convolution theorem from Wikipedia

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marked as duplicate by MBaz, Marcus Müller, lennon310, Peter K. May 30 at 15:59

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  • $\begingroup$ The page you linked has the proof. $\endgroup$ – Cris Luengo May 26 at 14:09

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