MATLAB code is given below in bold letters.
clc;
close all;
clear all;
% define w
w = [0 pi/6 3*pi/2 1.9*pi/2];
% define n
n = 1 : 50;
% define x1 and x2 and compute y1 and y2 using for loop
for
% different values of w
for k = 1:length(w)
% define x1 and x2
x1 = sin(w(k)*n);
x2 = cos(w(k)*n);
% now compute y1 and y2
y1 = 0.5*([zeros(1,length(x1)+1) x1]+[fliplr(x1)
zeros(1,length(x1)+1)]);
y2 = 0.5*([zeros(1,length(x1)+1) x1]-[fliplr(x1)
zeros(1,length(x1)+1)]);
% now plot the signals
figure;
subplot(211);
stem(-max(n):max(n),y1,'fill'); grid on;
xlabel('n');ylabel('Amplitude');title(['y1[n] for w =
',num2str(w(k))]);
subplot(212);
stem(-max(n):max(n),y2,'fill'); grid on;
xlabel('n');ylabel('Amplitude');title(['y2[n] for w =
',num2str(w(k))]);
end
The plots are given below
from the above fiures it is observed that y1[n] is symmeric about y axis which means that y1[n] is an even part of the signal x1. likewise y2[n] is anti-symmeric about y axis which means that y2[n] is an odd part of the signal x1
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