10. Let x[n] and y[n] be periodic signals with common period N, and let z[n] be their periodic convolution. (a) Verify that if ak, bk and ck are the Fourier coefficients of x[n], y[n] and z[n] respectively, then ck = Nakbk (b) Let x[n] = { sin(), 0 ≤ n ≤3 4≤ n ≤7 y[n] = (-)"; 0 ≤ n ≤7 be two signals that are periodic with period 8. Find the Fourier series representation for the periodic convolution of these signals.