The convolution sum is a fast way to find the coefficients of the polynomial resulting from the multiplication of two polynomials.

(a) Suppose x[n] = u[n] - u[n - 3] find its Z-transform X(z), a second order polynomial in z^-1.

(b) Multiply X(z) by itself to get a new polynomial Y(z) = X(z)X(z) = X²(z). Find Y (z).

(c) Do graphically the convolution of x[n] with itself and verify that the result coincides with the coefficients of Y (z).

(d) Use the conv function to find the coefficients of Y (z).