Abstract
In this chapter we will describe the design of infinite impulse response (IIR) digital filters. The impulse response of an IIR digital filter has an infinite extent or length or duration, hence the name IIR filters. Design of an IIR filter amounts to the determination of its impulse response sequence {h[n]} in the discrete-time domain or to the determination of its transfer function H(ejΩ) in the frequency domain. The design can also be accomplished in the Z-domain. In fact, this is the most commonly used domain. The theory of analog filters preceded that of digital filters. Elegant design techniques for analog filters in the frequency domain were developed much earlier than the development of digital filters. As a result, we will adopt some of the techniques used to design analog filters in designing an IIR digital filter. In order to facilitate the design of an IIR digital filter, one must specify certain parameters of the desired filter. These parameters can be in the discrete-time domain or in the frequency domain. Once the parameters or specifications are known, the task is to come up with either the impulse response sequence or the transfer function that approximates the specifications of the desired filter as closely as possible. In the discrete-time domain, one of the design techniques is known as the impulse invariance method. In the frequency domain, the design will yield a Butterworth or Chebyshev or elliptic filter. These three design procedures will result in a closed-form solution. Similarly, the impulse invariance technique will also result in a closed-form solution to the design of IIR digital filters. In addition to these analytical methods, an IIR digital filter can also be designed using iterative techniques. These are called the computer-aided design. Let us first describe the impulse invariance method of designing an IIR digital filter. We will then deal with the design in the frequency domain and the computer-aided design.
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Antoniou A (1993) Digital filters: analysis, design, and applications, 2nd edn. McGraw-Hill, New York
Charalambous C, Antoniou A (1980) Equalization of recursive digital filters. IEE Proc 127(Part G):219–225
Constantinides AC (1970) Spectral transformations for digital filters. Proc IEE 117:1585–1590
Deczky AG (1972) Synthesis of digital recursive filters using the minimum P error criterion. IEEE Trans Audio Electroacoust AU-20(2):257–263
Johnson M (1983) Implement stable IIR filters using minimal hardware, EDN
Kaiser JF (1963) Design methods for sampled data filters. Proceedings first annual Allerton conference on circuit and system theory, Chapter 7, pp 221–236
Kaiser JF (1965) Some practical considerations in the realization of linear digital filters. Proceedings third annual Allerton conference on circuit and system theory, pp 621–633
Kaiser JF (1966) Digital filters. In: Kuo FF, Kaiser JF (eds) System analysis by digital computer. Wiley, New York, pp 218–227
Mitra SK (2011) Digital signal processing: a computer-based approach, 4th edn. McGraw-Hill, New York
Mitra SK, Hirano K, Nishimura S, Sugahara K (1990) Design of digital bandpass/bandstop digital filters with tunable characteristics, Frequenz, 44, pp 117–121
Mitra SK, Neuvo Y, Roivainen H (1990) Design and implementation of recursive digital filters with variable characteristics. Int J Circuit Theory Appl 18:107–119
Oppenheim A, Schafer R, Buck J (1999) Discrete-time signal processing, 2nd edn. Prentice Hall, Upper Saddle River
Parks TW, Burrus CS (1987) Digital filter design. New York, Wiley
Rabiner LR, Gold B (1975) Theory and application of digital signal processing. Prentice Hall, Englewood Cliffs
Remez EY (1934) General computational methods of Chebyshev approximations, Atomic Energy Translation 4491, Vol. 198, pp 2063
Steiglitz K (1970) Computer-aided design of recursive digital filters. IEEE Trans on Audio Electroacoust 18(2):123
Vaidyanathan PP, Regalia PA, Mitra SK (1987) Design of doubly-complementary IIR digital filters using a single complex allpass filter, with multirate applications. IEEE Trans Circuits Syst CAS-34:378–389
Williams CS (1986) Designing digital filters. Prentice Hall, Englewood Cliffs
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Thyagarajan, K.S. (2019). IIR Digital Filters. In: Introduction to Digital Signal Processing Using MATLAB with Application to Digital Communications. Springer, Cham. https://doi.org/10.1007/978-3-319-76029-2_6
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