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## Convolution

Definition:Theconvolutionof two signals and in is denoted “” and defined by

Note that this iscyclicor “circular” convolution.^{8.2}The importance of convolution inlinear systems theoryis discussed in §8.7Convolution is

commutative, i.e.,

Proof:

where in the first step we made the change of summation variable , and in the second step, we made use of the fact that any sum over all terms is equivalent to a sum from to .

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