Aliasing and Nyquist Condition

Let us consider a simple sinusoidal signal

x(t) = 5sin(10t + 3)

This is a signal with an amplitude of 5, the angular frequency of 10 and phase of 3. The Nyquist condition demands that the angular frequency, mod(𝜔) ≤ pi/delta t.

Screen Shot 2018-11-22 at 3.10.15 PM

For the above figure 1, we took 𝜔 to be 10 and pi/delta t is 99.5, so the Nyquist condition satisfies and we do not see the aliasing. Here the sampling rate, Δ𝑡 is 0.0316.

Let us see what happens when we take the pi/delta t to be less than 𝜔.

Screen Shot 2018-11-22 at 3.10.52 PM.png

In this case, we took the sampling rate, Δ𝑡 to be 0.3307. Here the pi/delta t is 9.5000 which is less than 𝜔. Hence the Nyquist condition is not satisfied and there is a clear aliasing. The sinusoidal signal does not appear to be sinusoidal.

Figures

Matlab Codes:

clear; close all; clc
t=linspace(0,2*pi,20);
dt=t(3)-t(2)
omegaN=pi/dt
wf=5*sin(10*t+3);
plot(t,wf)
grid on
axis tight
xlabel('Time')
ylabel('Amplitude')
title('Plot of 5*sin(10t+3)')

—Utpal Kumar (IES,  Academia Sinica)

Published by

utpalkumaries

For any comments and suggestions, write to me at: utpalkumar50@gmail.com

One thought on “Aliasing and Nyquist Condition

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google+ photo

You are commenting using your Google+ account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s