Question about the Nyquist sampling rate

[Vagabond7]

I'm trying to look up sources on the nyquist sampling rate, but I keep finding this small subtle difference between sources, and I am not sure if it is laziness or some subtle point I am missing.

Sometimes I see the nyquist rate as Fs>2Fm and sometimes I see it as Fs>=2Fm. So is it the sampling rate is any frequency equal or greater than two times the max frequency, or does the sampling frequency have to be greater than two times the signal's max frequency? Or is there some subtlety that I am missing in the articles I am reading, and under some circumstances it is equal to or greater and others it has to be greater.

I feel like I am finding online sources that write it one way and some write it the other way, and I just want to make sure my understanding is exact. Thanks in advance.

 

[milesyoung]

It's a strict inequality, since, if you take the classic example of a sine wave sampled at exactly twice its frequency, you could have the two samples per period lie on the zero crossings, and you can't reconstruct the original signal from a sequence of zeros. In practice, however, you'd typically sample at a much higher frequency than dictated by this inequality.

You can get away with sampling below the Nyquist rate for a signal, by exploiting aliasing, if it has both a lower and upper frequency bound for its content (sometimes called a passband signal).

As a sidenote: Be careful about using 'Nyquist frequency' and 'Nyquist rate' interchangeably. There can be a difference depending on context.

 

[Vagabond7]

Thank you very much for the information, that clears everything up.

 

[Baluncore]

Shannon's sampling theorem says sample at twice the highest frequency present in the signal.

http://en.wikipedia.org/wiki/Nyquist–Shannon_sampling_theorem

If a function x(t) contains no frequencies higher than B cps, it is completely determined by giving its ordinates at a series of points spaced 1/(2B) seconds apart.
A sufficient sample-rate is therefore 2B samples/second, or anything larger. Conversely, for a given sample rate fs the bandlimit for perfect reconstruction is B ≤ fs/2 . When the bandlimit is too high (or there is no bandlimit), the reconstruction exhibits imperfections known as aliasing. Modern statements of the theorem are sometimes careful to explicitly state that x(t) must contain no sinusoidal component at exactly frequency B, or that B must be strictly less than ½ the sample rate. The two thresholds, 2B and fs/2 are respectively called the Nyquist rate and Nyquist frequency.

Nyquist had little to do with it.
http://en.wikipedia.org/wiki/Nyquist–Shannon_sampling_theorem#Why_Nyquist.3F

 

[milesyoung]

Shannon's sampling theorem says sample at twice the highest frequency present in the signal.

Modern statements of the theorem are sometimes careful to explicitly state that x(t) must contain no sinusoidal component at exactly frequency B, or that B must be strictly less than ½ the sample rate.