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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