6
Design and Implementation
of IIR Filters
We have discussed the design and implementation of digital FIR filters in the previous
chapter. In this chapter, our attention will be focused on the design, realization, and
implementation of digital IIR filters. The design of IIR filters is to determine the
transfer function H(z) that satisfies the given specifications. We will discuss the basic
characteristics of digital IIR filters, and familiarize ourselves with the fundamental
techniques used for the design and implementation of these filters. IIR filters have the
best roll-off and lower sidelobes in the stopband for the smallest number of coefficients.
Digital IIR filters can be easily obtained by beginning with the design of an analog
filter, and then using mapping technique to transform it from the s-plane into the z-
plane. The Laplace transform will be introduced in Section 6.1 and the analog filter will
be discussed in Section 6.2. The impulse-invariant and bilinear-transform methods for
designing digital IIR filters will be introduced in Section 6.3, and realization of IIR
filters using direct, cascade, and parallel forms will be introduced in Section 6.4. The
filter design using MATLAB will be described in Section 6.5, and the implementation
considerations are given in Section 6.6. The software development and experiments
using the TMS320C55x will be given in Section 6.7.
6.1 Laplace Transform
As discussed in Chapter 4, the Laplace transform is the most powerful technique used to
describe, represent, and analyze analog signals and systems. In order to introduce
analog filters in the next section, a brief review of the Laplace transform is given in
this section.
6.1.1 Introduction to the Laplace Transform
Many practical aperiodic functions such as a unit step function u(t), a unit ramp tu(t),
or an impulse train
I
kÀI
dt À kT do not satisfy the integrable condition given in
(4.1.11), which is a sufficient condition for a function x(t) that possesses a Fourier
Real-Time Digital Signal Processing. Sen M Kuo, Bob H Lee
Copyright # 2001 John Wiley & Sons Ltd
ISBNs: 0-470-84137-0 (Hardback); 0-470-84534-1 (Electronic)