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 convfunction to find the coefficients of Y(z).