FFT minimum sampling duration

In summary, you need to sample at a frequency over twice the original frequency in order to accurately resolve a 60Hz input signal. The number of samples you take is equal to the number of frequency 'bins' in the discrete Fourier transform. However, if you replace the number of samples with the length of time over which you sample the signal, you can see that your frequency resolution is actually 1/T.
  • #1
dmorris619
42
0
I am wondering what the minimum sampling duration must be in order to accurately resolve a 60Hz wave. I know the FFT works with periodic waves about the number N but I am not sure how this relates to say a sampling duration that is 1 half the sampling period of a 60 Hz wave. I'm worried that the duration will be so short that it cannot accurately resolve the wave. Also the nyquist rate will be 1MSPS so it far above the nyquist frequency.

Any guidance would be great.
 
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  • #2
i'm pretty sure you need to sample at a frequency of over two times the original frequency to prevent "aliasing"
 
  • #3
Im not talking aliasing or sampling rate I am talking duration of sampling or number of samples. Our sampling rate is high enough above the nyquist frequency I am just concerned we don't have enough samples to resolve a 60hz wave using an fft given the periodic nature of of the fft.
 
  • #4
Presumably your sample window is equal to or shorter than 1/sample-rate, no? Then you can't squeeze any more information out of a signal at the Nyquist frequency. Also you can't resolve phase information below 180deg at the Nyquist frequency.

If your sample-rate is some-many-multiples of 60Hz you will be able to get a more accurate representation of a 60Hz input signal, including harmonics and phase.

But that may not be what you are asking about?
 
  • #5
I think you'll have to come up with an objective measure of what you mean by 'accurately resolve'.

The number of frequency 'bins' that come out of the discrete Fourier transform is equal to the number of samples you take. So your frequency resolution will be Fs/N, where Fs is your sampling frequency and N is the number of samples you take. However, if you replace N with Fs*T, with T representing the length of time over which you sample the signal, you can see that your frequency resolution is actually 1/T (independent of the sampling frequency).

When I say frequency resolution, I mean the spacing between the frequency 'bins' in Fourier transformed signal. So, its not very simple to say how long you need to sample to acquire your signal, in order to 'accurately' resolve its frequency. In general, your signal won't fall neatly into one bin and so it will be distributed among multiple bins, which may or may not be a problem for you.

To complicate matters, the fact that you are taking a finite chunk of the signal means that you'll be introducing artifacts into the spectrum. An abrupt stop in sampling is equivalent to multiplying the 'true' signal by a rectangle function. That means you're convolving the spectrum with a sinc function (i.e. blurring it) in the frequency domain. The shorter your sampling time, the narrower the rectangle function will be, and correspondingly, the wider the sinc function will be in the frequency domain. So you can imagine if your signal is a perfect 60Hz sine wave, and you sample it over a very short period, you'll end up with a sinc function (as opposed to a delta) in the frequency domain, whose width gets larger as you lower the sampling time.
 

1. What is FFT minimum sampling duration?

The FFT (Fast Fourier Transform) minimum sampling duration refers to the shortest amount of time needed to accurately capture a signal or waveform using the FFT algorithm. It is the minimum duration required to sample a signal in order to avoid aliasing, which can lead to inaccurate frequency analysis.

2. How is FFT minimum sampling duration calculated?

FFT minimum sampling duration is calculated using the Nyquist-Shannon sampling theorem, which states that the sampling rate must be at least twice the highest frequency component present in the signal. The formula for calculating the minimum sampling duration is 1/(2*Fmax), where Fmax is the highest frequency component.

3. Why is FFT minimum sampling duration important?

FFT minimum sampling duration is important because it ensures accurate frequency analysis of a signal. If the sampling duration is too short, it can lead to aliasing and distort the frequency components of the signal. This can result in inaccurate analysis and interpretation of the data.

4. How does the FFT minimum sampling duration affect data analysis?

The FFT minimum sampling duration directly affects the accuracy of data analysis. If the sampling duration is too short, it can lead to inaccurate frequency analysis, which can result in incorrect conclusions about the data. It is important to use a sampling duration that is equal to or greater than the minimum required to avoid aliasing.

5. Can the FFT minimum sampling duration be reduced?

Yes, the FFT minimum sampling duration can be reduced by increasing the sampling rate. However, this may result in a larger amount of data to be processed, which can have implications for storage and processing capabilities. It is important to find a balance between the minimum sampling duration and the amount of data to be processed for accurate and efficient data analysis.

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