//clear//
//Example 5.1:Discrete Time Fourier Transform of discrete sequence
//x[n]= (a^n).u[n], a>0 and a<0
clear;
clc;
close;
// DTS Signal
a1 = 0.5;
a2 = -0.5;
max_limit = 10;
for n = 0:max_limit-1
  x1(n+1) = (a1^n);
  x2(n+1) = (a2^n);
end
n = 0:max_limit-1;
// Discrete-time Fourier Transform
Wmax = 2*%pi;       
K = 4;
k = 0:(K/1000):K;
W = k*Wmax/K;
x1 = x1';
x2 = x2';
XW1 = x1* exp(-sqrt(-1)*n'*W);
XW2 = x2* exp(-sqrt(-1)*n'*W);
XW1_Mag = abs(XW1);
XW2_Mag = abs(XW2);
W = [-mtlb_fliplr(W), W(2:1001)]; // Omega from -Wmax to Wmax
XW1_Mag = [mtlb_fliplr(XW1_Mag), XW1_Mag(2:1001)];
XW2_Mag = [mtlb_fliplr(XW2_Mag), XW2_Mag(2:1001)];
[XW1_Phase,db] = phasemag(XW1);
[XW2_Phase,db] = phasemag(XW2);
XW1_Phase = [-mtlb_fliplr(XW1_Phase),XW1_Phase(2:1001)];
XW2_Phase = [-mtlb_fliplr(XW2_Phase),XW2_Phase(2:1001)];
//plot for a>0
figure
subplot(3,1,1);
plot2d3('gnn',n,x1);
xtitle('Discrete Time Sequence x[n] for a>0')
subplot(3,1,2);
a = gca();
a.y_location ="origin";
a.x_location ="origin";
plot2d(W,XW1_Mag);
title('Magnitude Response abs(X(jW))')
subplot(3,1,3);
a = gca();
a.y_location ="origin";
a.x_location ="origin";
plot2d(W,XW1_Phase);
title('Phase Response <(X(jW))')
//plot for a<0
figure
subplot(3,1,1);
plot2d3('gnn',n,x2);
xtitle('Discrete Time Sequence x[n] for a>0')
subplot(3,1,2);
a = gca();
a.y_location ="origin";
a.x_location ="origin";
plot2d(W,XW2_Mag);
title('Magnitude Response abs(X(jW))')
subplot(3,1,3);
a = gca();
a.y_location ="origin";
a.x_location ="origin";
plot2d(W,XW2_Phase);
title('Phase Response <(X(jW))')