Convolution Theorem for the DTFT

The *convolution* of discrete-time signals
and
is defined
as

(3.22) |

This is sometimes called

The *convolution theorem* is then

(3.23) |

That is,

*Proof: *The result follows immediately from interchanging the order
of summations associated with the convolution and DTFT:

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