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,

A more elaborate example of a partial fraction expansion into complex one-pole sections is given in §3.12.1.

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