Determine whether the system is linear and time-invariant

Question

A discrete-time system is implemented by MATLAB function y=ltiwhich(x).

(a) Determine whether the system is linear and time-invariant. Hint: You can check the response to the input x[n] = (-1)n^u[n]. Why?

(b) If the system is LTI determine its impulse response h[n] and its frequency response H (ej^ω) using MATLAB.

(c) Estimate |H (ej^ω)| and ∠H (ej^ω) using (5.14) for ω = kπ/10, 0 ≤ k ≤ 10 and compare with the results obtained in (b).