Matched Z Transformation

The *matched z transformation* uses the same pole-mapping
Eq.(8.2) as in the impulse-invariant method, but the zeros
are handled differently. Instead of only mapping the poles of the
partial fraction expansion and letting the zeros fall where they may,
the matched

The factored form [452] of a transfer function

can be written as

The matched

to get

where the free gain is introduced to implement the desired normalization, such as matching dc gain. Note that the matched

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