The general second-order case with (the so-called
biquad section) can be written when
as
The delayed form of the partial fraction expansion is obtained by
leaving the coefficients in their original order. This corresponds
to writing as a ratio of polynomials in
:
Numerical examples of partial fraction expansions are given in §6.8.8
below. Another worked example, in which the filter
is converted to a set of parallel, second-order
sections is given in §3.11. See also §9.2 regarding
conversion to second-order sections in general, and §E.9.1 (especially
Eq. (E.22)) regarding
a state-space approach to partial fraction expansion.