Nyquist Rates

In order to find the Nyquist rate of a signal given x(t):

We will first find the fourrier transform X(W) and plot out its signal over a period of frequency Wm.

Once the Wm is found, then it is to be multiplied by two and that is the total given nyquist rate.


2Wm is known as the total Nyquist rate. Using the sampling theorem we know that if we let x(t) be a band limited signal with X(jW) = 0 for |W| > Wm, then x(t) is uniquely determined to be from X(nT): n=0,1,-1,2,-2...etc. as long as Ws > 2Wm

and Ws = $ \frac{2* \pi}{T} $

Since we have the Wm and the original signal to be recovered we know that the cutoff frequency is greater than Wm and less than Ws - Wm. We process this signal through a lowpass filter and receive the output signal that is exactly x(t).

Alumni Liaison

Ph.D. 2007, working on developing cool imaging technologies for digital cameras, camera phones, and video surveillance cameras.

Buyue Zhang