Question

% Illustration of Aliasing Effect in the Time-Domain

clf;
T = 0.1;f = 13;
n = (0:T:1)';
xs = cos(2*pi*f*n);
t = linspace(-0.5,1.5,500)';
ya = sinc((1/T)*t(:,ones(size(n))) - (1/T)*n(:,ones(size(t)))')*xs;
plot(n,xs,'o',t,ya);grid;
xlabel('Time, msec');ylabel('Amplitude');
title('Reconstructed continuous-time signal y_{a}(t)');
axis([0 1 -1.2 1.2]);

a. Run the program to generate both the discrete-time signal x[n] and its
continuous-time equivalent ya(t), and display them.
b. What is the range of t and the value of the time increment in the program?
What is the range of t in the plot? Change the range of t so as to display the
full range ya(t) being computed in the above program and run it again.
Comment on the plot generated after this change.

Answer 1

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SOLUTION

part a:

CODE:

clf; clc; close all; clear all;
T = 0.1; f = 13;
n = (0:T:1)';
xs = cos(2*pi*f*n);
t = linspace(-0.5,1.5,500)';
ya = sinc((1/T)*t(:,ones(size(n))) - (1/T)*n(:,ones(size(t)))')*xs;
% subplot(211)

plot(n,xs,'o',t,ya);
grid on;
xlabel('Time, msec');
ylabel('Amplitude');
title('Reconstructed time signal y(a)(t)');
axis([0 1 -1.2 1.2]);
legend('x(n)','y(t)')

OUTPUT SCREEN:

part b:

The range of t is defined in following line:

t = linspace(-0.5,1.5,500)';

The range of t is from -0.5 to 1.5 with increment of 0.0040 or we can also say that there are 500 samples used

Now increasing the range of t but keeping the number of samples equal to 500

CODE:

clf; clc; close all; clear all;
T = 0.1; f = 13;
n = (0:T:1)';
xs = cos(2*pi*f*n);
t = linspace(-0.5,1.5,500)';
ya = sinc((1/T)*t(:,ones(size(n))) - (1/T)*n(:,ones(size(t)))')*xs;
subplot(211)
plot(n,xs,'o',t,ya);
grid on;
xlabel('Time, msec');
ylabel('Amplitude');
title('Reconstructed time signal y(a)(t) for t =[-.5,1.5]');
axis([0 1 -1.2 1.2]);
legend('x(n)','y(t)')


t = linspace(-10,10,500)';
ya = sinc((1/T)*t(:,ones(size(n))) - (1/T)*n(:,ones(size(t)))')*xs;
subplot(212)
plot(n,xs,'o',t,ya);
grid on;
xlabel('Time, msec');
ylabel('Amplitude');
title('Reconstructed time signal y(a)(t)for t =[-10,10]');
axis([0 1 -1.2 1.2]);
legend('x(n)','y(t)')

OUTPUT SCREEN:

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