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