4. In this problem we derive two important properties of the continuous-time Fourier series: the multiplication property and Parseval's relations. Let x(t) and y(t) both be continuous-time periodic signals having period To and with Fourier series representations given by, ∞ x(t) Σ ακρόκωσε k=-∞ y(t) = brejkwat Σbkej k=-00 (a) Show that the Fourier series coefficients of the signal x(t) = x(t)y(t) = Ĉ are given by the discrete convolutions, k=-∞ ckej kwot Ck = Σ anbk-n- n=-∞ x₁(t) cos 20πt -2 -1 1 2 4 t (a) (b) Use the result of part (a) to compute the Fourier series coefficients of the signal x(t) depicted above. and (c) Suppose that y(t) equals x*(t). In this case express bk in terms of the coefficients ak use the result from part (a) to prove Parseval's relation for a periodic signal - that is, ∞ 10 √ | x(t)|² dt = Σ |ax|². To k=-∞