Let x[n] = 1+e j0n and y[n] = 1 + e j20 n be periodic signals of

Let x[n] = 1+e^jω0n and y[n] = 1 + e^j2ω0 n be periodic signals of fundamental period ω₀ = 2π/N, find the Fourier series of their product z[n] = x[n] y[n] by

(a) calculating the product x[n] y[n],

(b) using the periodic convolution of length N = 3 of the Fourier series coefficients of x[n] and y[n]. Is the periodic convolution equal to x[n] y[n] when N = 3? Explain.