In the system shown in the Figure P8.39, x1[n] and x2[n] are both causal, 32-point seque...

In the system shown in the Figure P8.39, x₁[n] and x₂[n] are both causal, 32-point sequences, i.e., they are both zero outside the interval 0 ≤ n ≤ 31. y[n] denotes the linear convolution of x₁[n] and x₂[n], i.e., y[n] = x₁[n] ∗ x₂[n].

(a) Determine the values of N for which all the values of y[n] can be completely recovered from x₅[n].

(b) Specify explicitly how to recover y[n] from x₅[n] for the smallest value of N which you determined in part (a).