To illustrate an example involving complex poles, consider the filter

where can be any real or complex value. (When is real, the filter as a whole is real also.) The poles are then and (or vice versa), and the factored form can be written as

Using Eq. (6.8), the residues are found to be

Thus,

More examples are given in §3.12.

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