Question

P2.19 A linear and time-invariant system is described by the difference equation y(n) 0.5y(n 10.25y(n 2)-x(n) + 2r(n - 1) + r(n -3) 1. Using the filter function, compute and plot the impulse response of the system over 0n100. 2. Determine the stability of the system from this impulse response. 3. If the input to this system is r(n) 5 3 cos(0.2Tm) 4sin(0.6Tn)] u(n), determine the 200 using the filter function response y(n) over 0 n

Answer 1

Matlab Script:

b = [1 2 0 1];
a = [1 -0.5 0.25];

xn = [1 zeros(1,100)]; %impulse input where it is 1 only at n=0

n = 0:100;
hn = filter(b,a,xn);

stem(n,hn);

b. As we can see from above figure that h[n] is approaching zero as n increasing hence the system is stable

n = 0:200;
xn = 5+(3*cos(0.2*pi*n))+(4*sin(0.6*pi*n));
figure();

yn = filter(b,a,xn);
stem(n,yn);