1. For the periodic rectangular signal y(t) as shown below, the Fourier series repre- sentation of y(t) can be expressed as y(t) = ks-00 where we = . 15 0 3 -1 3 Let N 2n(t) . k=- Please complete the following Matlab code (replace the four "?" by correct ones) and answer the questions. %Matlab code for Gibbs phenomenon clear all; N = 9:% configurable parameters t.d = 0.001; t = -3:t_d:3: y = zeros (1, length(t)):% rectangular signal y((-2.5+3)/t_d+1:(-1.5+3)/t_d) = ones (1, 1/t.d); y((-0.5+3)/t.d+1:(0.5+3)/t_d) = ones (1, 1/t_d); y((1.5+3)/t.d+1:(2.5+3)/t_d) = ones (1, 1/t.d); omega_0 = pi:% The fundamental period is 2. a_0 = ?: % Fourier series coefficients (k=0) x-N = a_0*ones (1. length(t)): %a_0 is a constant. for k = 1:N a k = ?; a_minus-k=a_k; %a_{-k} = a_k X_N = x_N + a_k*? + a_minus_k*?: end plot(t.y, 'r'); hold on plot(t, x-N,'b'); grid; legend ('Rectangular signal', 'x.N(+)'); xlabel('t'); ylabel (*x_N(+)'); axis ([-3 3-0.5 1.5l): (a) (10%) Find do (b) (10%) Find ar for k *0. (c) (10%) Find 0. (d) (10%) Find 1990.49) and 199 (0.5). (e) (10%) Find 1-0), 13(0), 41(0), 111 (0) and 21111(0). (f) (10%) Find (0.5), 13(0.5), 111(0.5), 11n (0.5) and 1111 (0.5). (g) (5%) Find the maximum value of (t) and tmax = arg maxosisi (t). (h) (5%) Find the maximum value of 13(t) and tmax = arg maxosesir(t). (i) (5%) Find the maximum value of r(t) and tmax = arg maxosasi Is(t). 6) (5%) Find the maximum value of x=(t) and (max = arg maxosisi zy(t). (k) (5%) Find the maximum value of Iu(t) and tmax = arg maxossi Iu(t). (1) (5%) Find the maximum value of su(t) and (max = arg maxo