Design of Recursive Digital Filter IIR Filters The

Design of Recursive Digital Filter (IIR Filters) The design of recursive digital filter required finding the transfer function of the filter which satisfies a given performance specifications. There are two general approaches used to design IIR filter. The most common is to design an analog IIR filter and then map it to an equivalent digital filter by bilinear transformation, impulse invariance method and, etc.

IIR filter design techniques rely on existing analog filters to obtain digital filters. these analog filters designate as prototype filter. Three prototypes are widely used: 1. .

Butterworth lowpass filters: This filter is characterized by the property that the magnitude response is flat in both passband stopband. The magnitude _squared response of an nth-order lowpass filter is given by

Design procedure of IIR filter Design prototype Butterworth low filter ransform the normilized lowpass filter to any other buterworth lowpass , highpass, bandstop filter The designed analog filter is convert to digital filer by bilinear transformation

the frequancy response is is obtianed by letting s=jw as where k=0, 1, …. 2 n-1 … (6)

pole plots for the Butterworth filter

Then the transfer function of Butterworth filter .

Example 13 -1: Solution: for order 2 the numbers of poles of H(s)H(-s) is given by k where k=0, 1, …. 2 n-1 ; there are 4 poles