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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Detailed derivation of the Discrete Fourier Transform (DFT) and its associated mathematics, including elementary audio signal processing applications and matlab programming examples.