Infinite Impulse Response IIR FILTER (IIR)

6. IIR FILTER.



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

EQUIPMENTS:
Software - MATLAB

Learning Objectives: To make the students familiar with designing concepts of FIR filter
with the use of MATLAB.

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.
bk and ak 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-->');

Finite Impulse Response FIR FILTER (FIR)

5. FIR FILTER.


AIM: To verify FIR filters.

EQUIPMENTS:
Constructor –MATLAB Software

Learning Objectives: To make the students familiar with designing concepts of FIR filter
with the use of MATLAB.

THEORY:
A Finite Impulse Response (FIR) filter is a discrete linear time-invariant system whose
output is based on the weighted summation of a finite number of past inputs. An FIR transversal
filter structure can be obtained directly from the equation for discrete-time convolution.
In this equation, x(k) and y(n) represent the input to and output from the filter at time n.
h(n-k) is the transversal filter coefficients at time n. These coefficients are generated by using
FDS (Filter Design Software or Digital filter design package).
FIR – filter is a finite impulse response filter. Order of the filter should be specified.
Infinite response is truncated to get finite impulse response. placing a window of finite length
does this. Types of windows available are Rectangular, Barlett, Hamming, Hanning, Blackmann
window etc. This FIR filter is an all zero filter.

PROGRAM:
%fir filt design window techniques
clc;
clear all;
close all;
rp=input('enter passband ripple');
rs=input('enter the stopband ripple');
fp=input('enter passband freq');
fs=input('enter stopband freq');
f=input('enter sampling freq ');
wp=2*fp/f;
ws=2*fs/f;
num=-20*log10(sqrt(rp*rs))-13;
dem=14.6*(fs-fp)/f;
n=ceil(num/dem);
n1=n+1;
if(rem(n,2)~=0)
n1=n;
n=n-1;
end
c=input('enter your choice of window function 1. rectangular 2. triangular 3.kaiser: \n ');
if(c==1)
y=rectwin(n1);
disp('Rectangular window filter response');
end
if (c==2)
y=triang(n1);
disp('Triangular window filter response');
end
if(c==3)
y=kaiser(n1);
disp('kaiser window filter response');
end

%LPF
b=fir1(n,wp,y);
[h,o]=freqz(b,1,256);
m=20*log10(abs(h));
subplot(2,2,1);plot(o/pi,m);
title('LPF');
ylabel('Gain in dB-->');
xlabel('(a) Normalized frequency-->');
%HPF

b=fir1(n,wp,'high',y);
[h,o]=freqz(b,1,256);
m=20*log10(abs(h));
subplot(2,2,2);plot(o/pi,m);
title('HPF');
ylabel('Gain in dB-->');
xlabel('(b) Normalized frequency-->');
%BPF

wn=[wp ws];
b=fir1(n,wn,y);
[h,o]=freqz(b,1,256);
m=20*log10(abs(h));
subplot(2,2,3);plot(o/pi,m);
title('BPF');
ylabel('Gain in dB-->');
xlabel('(c) Normalized frequency-->');
%BSF
b=fir1(n,wn,'stop',y);
[h,o]=freqz(b,1,256);
m=20*log10(abs(h));
subplot(2,2,4);plot(o/pi,m);
title('BSF');
ylabel('Gain in dB-->');
xlabel('(d) Normalized frequency-->')