Consider the discretetime LT1 system characterized by the fo

Consider the discrete-time LT1 system characterized by the following difference equation with input and initial conditions specified: y[n] - ay[n-1] = 4.5 x[n], with y[-1]=0, x[n] = sin(3 pi n/4). Write a function to plot the output signal y[n], n = 0, 1, 2, ..., 200 for a = 0.4, a = 0.8 and a = 1.1 Calculate (by hand) the system transfer function H(z), and determine its poles and zeros. What happens when a = 1.1? Explain this behavior.

Solution

function y= myfunction(a)

y(0)=0;

2) take z transform

Y(z)=4.5*x(z)/(1-a*z^-1);

H(z)= 4.5/(1-az^-1);

Pole is at z= a,

Zero is at z=0.