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.

Alumni Liaison

Ph.D. on Applied Mathematics in Aug 2007. Involved on applications of image super-resolution to electron microscopy

Francisco Blanco-Silva