Question about the Nyquist sampling rate

In summary: The two thresholds, 2B and fs/2 are respectively called the Nyquist rate and Nyquist frequency.In summary, the Nyquist sampling rate is defined as twice the highest frequency present in the signal, and is also known as the Nyquist rate or Nyquist frequency. It is necessary for perfect reconstruction of the signal and can be expressed as B ≤ fs/2, where B is the highest frequency and fs is the sample rate. However, modern statements of the theorem often include additional criteria to ensure accurate reconstruction.
  • #1
Vagabond7
50
11
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.
 
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  • #2
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.
 
  • #3
Thank you very much for the information, that clears everything up.
 
  • #4
Shannon's sampling theorem says sample at twice the highest frequency present in the signal.

http://en.wikipedia.org/wiki/Nyquist–Shannon_sampling_theorem
Wikipedia said:
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
 
  • #5
Baluncore said:
Shannon's sampling theorem says sample at twice the highest frequency present in the signal.
Wikipedia said:
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.
 

Related to Question about the Nyquist sampling rate

1. What is the Nyquist sampling rate?

The Nyquist sampling rate, also known as the Nyquist frequency, is the minimum rate at which a signal needs to be sampled in order to accurately reconstruct the original signal. It is named after the American engineer Harry Nyquist.

2. Why is the Nyquist sampling rate important?

The Nyquist sampling rate is important because it determines the quality of the reconstructed signal. If the sampling rate is too low, the reconstructed signal will be distorted and inaccurate. In order to avoid this, it is necessary to sample at or above the Nyquist rate.

3. How is the Nyquist sampling rate calculated?

The Nyquist sampling rate is calculated by taking twice the highest frequency component in the signal. This is based on the Nyquist-Shannon sampling theorem, which states that in order to avoid aliasing (the distortion of high frequency signals), the sampling rate must be at least twice the highest frequency component.

4. Can the Nyquist sampling rate be exceeded?

Yes, the Nyquist sampling rate can be exceeded. In fact, modern technology often samples at rates much higher than the Nyquist rate in order to improve the accuracy and quality of the reconstructed signal. However, it is important to note that sampling above the Nyquist rate does not improve the signal quality if the signal does not contain frequencies above the Nyquist frequency.

5. What happens if the Nyquist sampling rate is not met?

If the Nyquist sampling rate is not met, aliasing will occur. Aliasing is when high frequency components in the signal are misrepresented as low frequency components, resulting in a distorted and inaccurate reconstructed signal. This can be avoided by properly sampling at or above the Nyquist rate.

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