Commutativity of Convolution

Convolution (cyclic or acyclic) is *commutative*, *i.e.*,

*Proof: *

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 0 to .

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Center for Computer Research in Music and Acoustics (CCRMA), Stanford University