The input of a discrete-time system is x[n] = u[n] − u[n − 4] and the  impulse of the system is h[n] = δ[n] + δ[n − 1] + δ[n − 2]

(a) Calculate the DFTs of h[n], x[n] of length N = 7. Call them H(k) and X(k). Calculate X(k) H(k) = Ŷ(k)

(b) If y(n) = (x∗h) [n], would you expect ŷ[n] = y[n]? Explain. If you  had chosen the lengths of the DFTs to be N = 4 would you have  had the circular and the linear convolutions coincide? Explain.