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:

[How to cite this work] [Order a printed hardcopy] [Comment on this page via email]

Copyright ©

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