Page 398 - Analog and Digital Filter Design

HAPTER 17

IIR FILTER DESIGN

Infinite impulse response (IIR) filters are more efficient than FIR filters because,
for a given frequency response, they require fewer delay elements, adders, and
multipliers. The disadvantage of IIR filters is their nonlinear phase response
(nonconstant group delay). Group delay has been discussed previously in
Chapters 2 and 9 in relation to analog filters: a nonconstant group delay means
that not all frequencies experience the same delay. Thus, impulses containing
components with a wide range of frequencies will be distorted when passed
through an IIR filter.

Most IIR filters are designed using an analog filter model. Analog filter models
are the familiar Butterworth, Chebyshev, Cauer (Elliptic). Inverse Chebyshev,
and Bessel types. Generally speaking. Bessel models are not converted into
digital filters. You may remember from Chapters 2 and 9 that the advantage of
a Bessel response in an active or passive linear filter is the constant group delay,
at the expense of a poor skirt response (the filter attenuation increases very
slowly). FIR filters can produce a constant group delay with far superior skirt
response, so they are used where group delay is important.

The linear frequency response formulae H(m) can be converted into the digital
equivalent using Impulse Invariant, Step Invariant, or Bilinear Transformation.
Only the bilinear transform provides a general-purpose conversion function that
can be used for lowpass, highpass, bandpass. and bandstop responses. The
impulse invariant and step invariant conversion functions are quite difficult to
apply and can only be used for lowpass filters (and bandpass with great care):
these conversion functions cannot be used with highpass or bandstop responses.
For these reasons, only bilinear transforms are considered in this chapter.

The basic IIR filter is based on the biquadratic (biquad) structure, which is
shown in Figure 17.1. The delay elements are denoted as l/z in this diagram.
The liz term is sometimes written as z-', especially in transfer functior
equations.