Consider the discrete-time signal x[n] = u[n] − u[n − M] where M is a positive integer.

(a) Let M = 1, calculate and sample the DTFT X(e^jω) in the frequency domain using a sampling frequency 2π/N with N = M to obtain the DFT of length N = 1.

(b) Let N = 10, still M = 1, sample the DTFT to obtain the DFT and carefully plot X(e^j2πk/N) = X[k] and the corresponding signal. What would happen if N is made 1024, what would be the differences with this case and the previous one? Explain.

(c) Let then M = 10, and N = 10 for the sampling of the DTFT. What does X[k] imply in terms of aliasing? Comment on what would happen if N > > 10, and when N < 10.