Given that the Z-transform of  a discrete-time cosine A cos(ω₀n) u[n] is

(a) Use the given Z-transform to find a difference equation whose output y[n] is a discrete-time cosine A cos(ω₀ n) and input x[n] = δ[n]. What should you use as initial conditions?

(b) Verify your algorithm by generating a signal  y[n] = 2 cos(Ï€n/2) u[n] by implementing your algorithm in  MATLAB. Plot the input and the output signals x[n] and y[n].

(c) Indicate how to change your previous algorithm to generate a  sine function y[n] = 2 sin(Ï€n/2) u[n]. Use MATLAB to find y[n],  and to plot it.

Transcribed Image Text:

A(1 – cos(@o)z¯') -2 1– 2 cos(@o)z'+z¯