A window is a signal w[n] that is used to highlight part of another signal. The windowing process consists in multiplying an input signal x[n] by the window signal w[n], so that the output is y[n] = x[n] w[n]. There are different types of windows used in signal processing; one of them is the so-called rectangular window which is given by

w[n] = u[n] − u[n − N]

(a) Determine whether the rectangular windowing system is linear. Explain.

(b) Suppose x[n] = nu[n], use MATLAB to plot the output y[n] of the windowing system (with N = 6).

(c) Let the input be x[n − 5], use MATLAB to plot the corresponding output of the rectangular windowing system, and indicate whether the rectangular windowing system is time-invariant.