The MATLAB code defines a discrete-time signal x[n] and plots it along with shifted (x[n-2]), modulated (x[n]u[2-n]), and even/odd parts of the signal. The code generates the plots by: 1) defining x[n] on domain n=-6 to 6; 2) plotting the original and transformed signals using STEM; and 3) decomposing x[n] into its even and odd parts by adding/subtracting the signal with its time-reversed version. The plots generated include those for the problems (a), (d), (g), and (h).

1. DISCRETE – TIME SIGNALS PLOTTING ON MATLAB
EXAMPLE
Solution by: MartinWachiye Wafula
MultimediaUniversity of Kenya
wachiyem@gmail.com
Problem:
Using MATLAB, producethe plot for (a), (d), (g) and (h)
Solution:
The code on MATLAB is as shownbelow:
%DISCRETE-TIME SIGNALS
%Author: Martin Wachiye Wafula
% Multimedia University of Kenya
%Date: 15th February, 2017
n = -6:6;
%The original signal x[n]
xn =((n+1)==0)+ (n==0)+ ((n-1)==0)+ ((n-2)==0)+ ...
0.5*(((n-3)==0)+ ((n-4)==0));
subplot(3,2,1)
stem(n,xn,'filled'), xlabel('n'), ylabel('x[n]')
title('plot of x[n]'), grid
%x[n] could also be plotted using the code below
% xn1 = ((n+1)==0)+(n>=0)-((n-3)>=0)+0.5*(((n-3)>=0)-((n-5)>=0));
%stem(n,xn1,'filled')
%(a) signal x[n-2]
xn_a = (((n-2)+1)==0)+ ((n-2)==0) + (((n-2)-1)==0) + ...
(((n-2)-2)==0) + 0.5*((((n-2)-3)==0) + (((n-2)-4)==0) );

2. subplot(3,2,2)
stem(n,xn_a,'filled'), xlabel('n'), ylabel('x[n-2]')
title('plot(a) x(n-2)'),grid
%signal (d): x[n]u[2-n]
xn_d = xn .*((2-n)>=0);
subplot(3,2,3)
stem(n,xn_d,'filled'), xlabel('n'), ylabel('x[n]u[2-n]')
title('plot(d) x[n]u[2-n]'),grid
% to obtain odd and even part of the signal x[n]
xN = fliplr(xn); %reversed version of x[n] i.e x[-n]
xe = (xn + xN)/2; %computing the even part
xo = (xn - xN)/2; %computing the odd part
ver = xn - (xe + xo) % to verify our decomposition
subplot(3,2,4)
stem(n,xe,'filled'), xlabel('n'), ylabel('xe[n]'),axis([-6 6 -1 1.5])
title('(g) Even Part'), grid
subplot(3,2,5)
stem(n,xo,'filled'), xlabel('n'), ylabel('xo[n]'),axis([-6 6 -1 1.5])
title('(h) Odd Part'), grid
The plots obtainedfrom running the code are as depictedby the screenshot
below: