Down-sampling and DTFT—Consider the pulses x1[n] = u[n]−u[n − 20] and x2[n] = u[n] − u[n − 10], and their product x[n] = x1[n]x2[n]. (a) Plot the three pulses. Could you say that x[n] is a down-sampled version of x1[n]? what would be the down-sampling rate? Find X1(e jω). (b) Find directly the DTFT of x[n] and compare it to X1(e jω/M), where M is the down-sampling rate found above. If we down-sample x1[n] to get x[n], would the result be affected by aliasing? Use MATLAB to plot the magnitude DTFT of x1[n] and x[n].