Convolution Theorem
Convolution in the time domain equals pointwise multiplication in the frequency domain, and vice versa; this turns the O(N²) work of filtering an LTI system into two transforms and a multiplication, and explains why windowing (multiplication) smears spectra (convolution).
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Convolution in the time domain equals pointwise multiplication in the frequency domain, and vice versa; this turns the O(N²) work of filtering an LTI system into two transforms and a multiplication, and explains why windowing (multiplication) smears spectra (convolution).
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