Chapter 12 - Introduction to the Design of Discrete Filters

Abstract

Filtering changes the frequency content of an input signal. In the discrete-time domain, two types of filters designs are: the Infinite Impulse Response (IIR) filter, and the Finite Impulse Response (FIR) filter. Discrete filters are implemented using software or dedicated hardware and minimal direct, cascade and parallel forms. 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, classical analog filter methods together with the bilinear transformation mapping the analog s-plane into the Z-plane are used to design low-pass filters. Frequency transformations allow for the design of other filters. 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. Images are filtered using classical space filters and the conventional frequency domain filters. Edge detection, de-blurring, de-noising, and compression of images are possible using two-dimensional filters. Design of one and two-dimensional filters are illustrated using MATLAB.