Chapter 12 - Introduction to the Design of Discrete Filters

Abstract

According to the eigenfunction property of LTI systems, filtering changes the frequency content of an input signal. In the discrete-time domain, two types of filters designs are possible: the infinite impulse response (IIR) filter resulting from rational approximation, and the finite impulse response (FIR) filter that results from polynomial approximation. These discrete filters are implemented using software or dedicated hardware and minimal direct, cascade, and parallel forms. The filter design consists in specifying a desired magnitude or impulse response followed by rational or polynomial approximation to obtain a stable and realizable filter. For IIR filters, the classical analog filter design methods together with the bilinear transformation, that maps the analog s-plane into the Z-plane, are used to design low-pass filters. Frequency transformations allow design of other filters. Given that the FIR filters are unique to the discrete domain, the approximation procedures for FIR filters are unique to that domain. A basic design uses windowing. The effect of different windows and the linearity of the phase are discussed. Design of IIR and FIR filters are illustrated using MATLAB.