Convolution Theorem

The *convolution theorem for z transforms* states that for any (real or
complex) signals and ,

*Proof: *

The convolution theorem provides a major cornerstone of linear systems theory. It implies, for example, that any LTI filter (recursive or nonrecursive) can be implemented by convolving the input signal with the impulse response of the filter, as shown in the next section.

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

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