4. (16 points) Let $x[n] = \{1, -2, 1, 2\}$, $0 \le n \le 3$ and $h[n] = \{2, 1, 0, 0, -1\}$, $0 \le n \le 4$.
(a) (6 points) Determine $y[n] = x[n] \circledast h[n]$. Show details for full credit.
(b) (6 points) Determine the 5-point circular convolution $z[n] = x[n] \stackrel{5}{\circledast} h[n]$. Show details for full credit.
(c) (4 points) What is the smallest value of N, such that $x[n] \stackrel{N}{\circledast} h[n] = x[n] \circledast h[n]$? Verify your choice of
N by carrying out the N-point circular convolution.