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Real-Time Digital Signal Processing - Chapter 6: Design and Implementation of IIR Filters

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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 | 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 6 Design and Implementation of HR 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 tuff or an impulse train S t kT do not satisfy .