Question

(c) Define the K partial sum approximation to z(t) as K(t)Bc( Use Matlab to evaluate and plot two periods of the K-th term in this sum and plot ax(t) for K1,3,7,29, and 99. Submit the term values, the plots, and the Matlab code generated to obtain the results. xl4) -I Figure 1: Matlab Problem 1

Answer 1

The sianal t) s even Sammetsi 4(2"cm2 +4@s.(np).'...e«-5〕 Sin (Tn

MATLAB CODE:

clc
clear all
close all
K = [1 3 7 29 99];
t = -1:0.01:1;
T=1;
for i=1:length(K)
x=0;
for n = 1:1:K(i)
a0 = 0;
an=8*(sin(pi*n/2)).^2./(pi*n).^2;
bn=0;
x = x+ an.*cos(2*pi*n.*t/T)+bn.*sin(2*pi*n.*t/T);
end
plot(t,x,'color',rand(1,3))
hold on
end
legend('K=1','K=3','K=7','K=29','K=99')
xlabel('time');
ylabel('amplitude');

Plot:

0.8ト 0.6 0.4 0.2 K-3 K-29 K-99 -0.2 0.4 0.6 0.8 -1 1 0.8 0.6 -0.4 0.2 0 0.2 0.4 0.6 0.8 1 time