(from Eq. (3.1), diagrammed in Fig.3.1). While this
structure, formally known as ``direct form I'', happens to be a good
choice for digital comb filters, there are many other structures to
consider in other situations. For example, it is often desirable,
for numerical reasons, to implement low-pass, high-pass,
and band-passfilters as series second-order sections.
On the other hand, digital filters for simulating the vocal
tract (for synthesized voice applications) are typically
implemented as parallel second-order sections. (When the order
is odd, there is one first-order section as well.)
The coefficients of the first- and
second-order filter sections may be calculated from the poles and
zeros of the filter.

We will now illustrate the computation of a parallel second-order
realization of our example filter
. As discussed above in §3.10, this filter has five
poles and three zeros. We can use the partial fraction
expansion (PFE), described in §6.8, to expand the transfer
function into a sum of five first-order terms:

where, in the last step, complex-conjugate one-pole sections are
combined into real second-order sections. Also, numerical values are
given to four decimal places (so `' is replaced by `' in
the second line). In the following subsections, we will plot the
impulse responses and frequency responses of the first- and
second-order filter sections above.