2) a) Transfer function:
Apply z transform to the difference equation,
Y(z)=1.5 z-1 Y(z) - 0.56 z-2 Y(z) + X(z) -0.2 z-1X(z)
Y(z)[1-1.5 z-1+0.56 z-2 ]= X(z)[1 -0.2 z-1]
Y(z) [1 -0.2 z-1]
H(z)= ------ = _______________
X(z) [1-1.5 z-1+0.56 z-2 ]
MATLAB:
clc;close all;clear all;
b=[1 -0.2]
a=[1 -1.5 0.56]
N=50
n=0:1:N-1
figure;
x=ones(1,N)
y=filter(b,a,x)
subplot(211)
stem(n,y,'r')
xlabel('n')
ylabel('y(n)')
title('Response using filter command')
subplot(212)
%from manually calculated analytical expression of y(n)
y=((-24*(0.8.^n))+(11.66 *(0.7.^n))+13.33).*(n>=0)
stem(n,y,'m');xlabel('n')
ylabel('y(n)')
title('from manually calculated analytical expression of y(n)')
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