Consider the circular convolution  of two signals x[n] = n, 0 ≤ n ≤ 3 and y[n] = 1, n = 0, 1, 2 and zero for n = 3.

(a) Compute the convolution sum or linear convolution of x[n] and  y[n]. Do it graphically and verify your results by multiplying the DFTs of x[n] and y[n].

(b) Use MATLAB to find the linear convolution. Plot x[n], y[n] and the  linear convolution z[n] = (x^∗y) [n].

(c) We wish to compute the circular convolution of x[n] and y[n] for different lengths N = 4, N = 7, and N = 10. Determine for which  of these values the circular and the linear convolutions coincide.  Show the circular convolution for the three cases. Use MATLAB to  verify your results.

(d) Use the convolution property of the DFT to verify your result in the  above part of the problem.