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skynelson
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- TL;DR Summary
- Convolving two signals, g and h, of lengths X and Y respectively, results in a signal with length X+Y-1. How can the length of an output signal of convolution be different from the input signals , given the contents of the Convolution Theorem? Thank you!
Convolving two signals, g and h, of lengths X and Y respectively, results in a signal with length X+Y-1. But through convolution theorem, g*h = F^{-1}{ F{g} F{h} }, where F and F^{-1} is the Fourier transform and its inverse, respectively. The Fourier transform is unitary, so the output signal is the same length as the input signal for that operation. The prescribed pointwise multiplication also requires signals of the same length (I believe the smaller will be padded to match the larger if needed).
How can the length of an output signal of convolution be different from the input signals , due to the Convolution Theorem?
How can the length of an output signal of convolution be different from the input signals , due to the Convolution Theorem?