IIR filter design - Continuous and Discrete Time Signals and Systems - page 713

CHAPTER

16

IIR filter design

Based on the length of the impulse response h [ k ], Chapter 14 classified digital
(or “discrete-time”) filters into two categories: finite impulse response (FIR)
filters and infinite impulse response (IIR) filters. The design techniques for
the FIR filter, with an impulse response h [ k ] of finite length, were covered in
Chapter 15. In this chapter, we present design methodologies of the IIR fil-
ters. A common technique used to design IIR filters is based on mapping the
DT frequency specifications H ( Ω ) of the IIR filters in the Ω domain to the
CT frequency specifications H ( ω ) specified in the ω domain. Based on the
transformed specifications, a CT filter is designed, which is then transformed
back into the original DT frequency Ω domain to obtain the transfer func-
tion of the required IIR filter. In this chapter, we present two different DT to
CT frequency transformations. The first method is referred to as the impulse
invariance transformation, which provides a linear transformation between the
DT and CT frequency domains. At times, the impulse invariance transforma-
tion suffers from aliasing, which may lead to deviations from the original DT
specifications. An alternative to the impulse invariance transformation is the
bilinear transformation, which is a non-linear mapping between the CT and DT
frequency domains. The bilinear transformation eliminates aliasing to a large
extent.
A classical problem in the design of digital filters is the selection between
FIR and IIR filters. While both types of filters can be used to satisfy a given set
of specifications, the order N of IIR filters is in general much lower than that of
FIR filters. As a consequence of the lower order N , the IIR filters have reduced
implementation complexity and less propagation delay when compared with
FIR filters designed for the same specifications. However, IIR filters are imple-
mented using feedback loops, resulting in transfer functions with a significant
number of poles. IIR filters are, therefore, susceptible to instability issues when
realized on finite-precision DSP boards. In addition, IIR filters have a non-linear
phase, whereas FIR filters can be designed with a linear phase. An appropriate
digital filter type is selected based on the requirement of a given application.

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