IIR filters Matlab code

AIM

To design and implement IIR (LPF/HPF)filters.

EQUIPMENTS:

Operating System         – Windows XP

Constructor                  - Simulator

Software                      - CCStudio 3 & MATLAB 7.5

THEORY:

The IIR filter can realize both the poles and zeroes of a system because it has a rational transfer function, described by polynomials in z in both the numerator and the denominator:

                                         

The difference equation for such a system is described by the following:

M and N are order of the two polynomials

b_k  and a_k are the filter coefficients. These filter coefficients are generated using FDS (Filter Design software or Digital Filter design package).

IIR filters can be expanded as infinite impulse response filters. In designing IIR filters, cutoff frequencies of the filters should be mentioned. The order of the filter can be estimated using butter worth polynomial. That’s why the filters are named as butter worth filters. Filter coefficients can be found and the response can be plotted.

PROGRAM :

%  IIR filters LPF & HPF

clc;

clear all;

close all;

disp('enter the IIR filter design specifications');

rp=input('enter the passband ripple');

rs=input('enter the stopband ripple');

wp=input('enter the passband freq');

ws=input('enter the stopband freq');

fs=input('enter the sampling freq');

w1=2*wp/fs;w2=2*ws/fs;

[n,wn]=buttord(w1,w2,rp,rs,'s');

c=input('enter choice of filter 1. LPF 2. HPF \n ');

if(c==1)

    disp('Frequency response of  IIR LPF is:');

[b,a]=butter(n,wn,'low','s');

end

if(c==2)

    disp('Frequency response of  IIR HPF is:');

[b,a]=butter(n,wn,'high','s');

end

w=0:.01:pi;

[h,om]=freqs(b,a,w);

m=20*log10(abs(h));

an=angle(h);

figure,subplot(2,1,1);plot(om/pi,m);

title('magnitude response of  IIR filter is:');

xlabel('(a) Normalized freq. -->');

ylabel('Gain in dB-->');

subplot(2,1,2);plot(om/pi,an);

title('phase response of  IIR filter is:');

xlabel('(b) Normalized freq. -->');

ylabel('Phase in radians-->');

 RESULT :