% Analog Signal
Dt = 0.00005;
t = -0.005:Dt:0.005;
xa = exp(-1000*abs(t));
% Discrete-time Signal
Ts = 0.001; n = -5:1:5;
x = exp(-1000*abs(n*Ts));
% Discrete-time Fourier transform
K = 500; k = 0:1:K;
w = pi*k/K;
X = x * exp(-j*n'*w);
X = real(X);
w = [-fliplr(w), w(2:K+1)];
X = [fliplr(X), X(2:K+1)];
subplot(1,1,1)
subplot(2,1,1);plot(t*1000,xa);
xlabel('t in msec.'); ylabel('xa(t)')
title('Discrete Signal'); hold on
stem(n*Ts*1000,x); hold off
subplot(2,1,2);plot(w/pi,X);
xlabel('Frequency in pi units'); ylabel('X(w)')
title('Discrete-time Fourier Transform')