From Eq. (6.5), we have , so that the frequency response is

and

where

and the DTFT is as defined in Eq. (7.1).

From the above relations, we may express the frequency response of any IIR filter as a ratio of two finite DTFTs:

This expression provides a convenient basis for the computation of an IIR frequency response in software, as we pursue further in the next section.

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