This page will talk about the important property of sampling theorem.
Consider the samples $ x(nT) $ for n = 0,-1,1,-2,2,...
if
- $ T < \frac{1}{2} \left (\frac{2\pi}{w_m} \right )\, $
then $ x(t) $ can be uniquely recovered from its samples. In this case, T is the sampling period, and $ \frac{2\pi}{T} $ (or $ w_s $) is the sampling frequency.
The important fact is that
- $ T < \frac{1}{2}\frac{2\pi}{w_m} $
- $ 2w_m < \frac{2\pi}{T} $
but we mentioned before that $ w_s = \frac{2\pi}{T} $ therefore,
- $ 2w_m < w_s $
In which $ 2w_m $ is called the Nyquist rate.
