Question

x[ri] -9 63 3 9 12 n 1. For the periodic DT signal shown in Top, a) determine the Fourier Series Coefficients. b) Use MATLAB to generate a spectral plot (magnitude plot and a separate phase plot). c) Use MATLAB to generate and plot the signal as a DTFS expansion of the periodic signal. Plot over an interval containing several periods. Make sure to include the MATLAB code

2.For the periodic DT signal shown in Top, a) determine the Fourier Series Coefficients. b) Use MATLAB to generate a spectral plot (magnitude plot and a separate phase plot). c) Use MATLAB to generate and plot the signal as a DTFS expansion of the periodic signal. Plot over an interval containing several periods. Make sure to include the MATLAB code

Answer 1

Cl Pe od N ς sample coectent t given by 2. Ск .ell e "jkst.) e-a (9 e + 씻(-2) +ス(o) + 6 3 e 3

%%% Matkab code %%%%

clc;
clear all;
close all;
format long

%%% b)
k=0:5;
Ck=1/6*(3+4*cos(pi/3*k)+2*cos(2*pi/3*k));

figure;
subplot(2,1,1);
stem(k,abs(Ck));
xlabel('K');
ylabel('|Ck|');
title('Magbitude plot');
subplot(2,1,2);
stem(k,angle(Ck));
xlabel('K');
ylabel('phase(Ck)');
title('Phase Plot');

%%%% c) DTFS Expansion of signal
xn=0;
n=-15:15;
for l=1:length(k)
    xn=xn+Ck(l)*exp(i*2*pi/6*k(l)*n);
end
figure;
stem(n,abs(xn));
xlabel('n');
ylabel('xn');
title('DTFS Expansion of signal');

OUTPUT:

Magbitude plot 1.50 8 0.5 0 0.5 1 15 2 2.5 3 3.54 4.5 5 Phase Plot 0 0.5 15 22.53 3.5 4 4.5 5

DTFS Expansion of signal 2.5 2p 1.5 0.5 -15 -10 -5 0 10 15