Analytical expression for y(n)
MATLAB:
clc;close all;clear all;
b=conv([1,1],[1 0.5])
a=conv(conv([1 -0.5],[1,-0.9]),[1,-0.8])
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 the analytical expression of y(n)
y=(((-25*(0.5.^n))+(-665 *(0.9.^n))+(390 *(0.8.^n))+(300
*(1.^n))).*(n>=0))
stem(n,y/max(y),'m');xlabel('n')
ylabel('y(n)')
title('from the analytical expression of y(n)')
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