Infinite impulse response digital filters

This chapter reviews the realisation of analogue low-pass filters using Butterworth and Chebyshev polynomials to control the pole/zero placement positions and consequent frequency response. It investigates the differences in the passband shape and transition band roll-off rate for these particular prototype filter designs. Digital filter design is then introduced via the difference equation of Chapter 4 and the various filter structures are explored. This chapter concentrates on the design approaches for realising infinite impulse response (IIR) digital filters, showing how the Butterworth and Chebyshev prototype designs are developed into practical digital filters via the bilinear z-transform..Finally there is a brief discussion of some of the limitations imposed on the resulting frequency response by finite precision arithmetic effects in these digital filters.