Let us consider a simple sinusoidal signal
x(t) = 5*sin(10*t + 3)
This is a signal with amplitude of 5, angular frequency of 10 and phase of 3. The Nyquist condition demands that the angular frequency, mod(𝜔) ≤ pi/delta t.
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.
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.
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)