How to obtain the low frequency component as accurately as possible?

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Discussion Overview

The discussion revolves around methods for accurately obtaining low frequency components from high sample rate data. Participants explore various techniques, including the use of FFT (Fast Fourier Transform) and low-pass filtering, while considering the implications of sampling rates and data length.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant suggests that low frequency components should be captured well in high sample rate data, questioning the utility of low-pass filtering.
  • Another participant emphasizes the importance of using a long FFT for achieving extreme low frequency resolution.
  • A different viewpoint proposes that digital filtering can be an effective solution, highlighting the limitations imposed by the low frequency performance of the sampling circuit.
  • Concerns are raised about the non-critical nature of the Nyquist anti-aliasing filter's high frequency performance.
  • It is noted that frequency resolution from an FFT is determined by the total time covered by the sampled data, rather than the sampling rate itself.
  • One participant mentions that increasing the sampling time can yield more frequency bins in the FFT output.
  • There is a suggestion that there may be alternative methods to estimate frequency components that could be more precise with less data, though the specifics of the original problem are unclear.

Areas of Agreement / Disagreement

Participants express differing views on the necessity and effectiveness of low-pass filtering and the methods for achieving low frequency resolution. The discussion remains unresolved regarding the best approach to accurately obtain low frequency components.

Contextual Notes

Participants acknowledge the potential limitations of the sampling circuit and the implications of data length on frequency resolution, but do not resolve these issues.

jollage
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I have data sampled at very high sample rate, which means that the high frequency components are probably well resolved. But I also want to look at the low frequency component, how to obtain them as accurately as possible? I do fft directly or I have to do low-pass filter first?
 
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Unless you have aliasing the low frequency components should be captured just fine in your data. Low pass filtering won't do anything useful for you. The one thing to think about is how you want to do your FFT. If you want extreme low frequency resolution you will need to use a long FFT to get your desired FFT bin size.
 
Once you have your enormous set of samples, due to highly over-sampling, then you can filter digitally and get your answer. That would be the cheapest solution and it would not involve the cost of extra analogue components, with all the disadvantages they introduce.
But remember, the answer you will get will only be as good as the low frequency performance of your sampling circuit will allow.
 
An additional thing; your Nyquist anti-aliasing filter can be very non critical in its high frequency performance.
 
The frequency resolution from an FFT depends on the total time covered by the sampled data, not on the sampling rate. The sampling rate affects the frequency range, but not the frequency resolution.

Unless you have literally billions of data points, there is no reason to throw away any data by resampling. Doing an FFT with millions of points is no big deal on a modern PC.
 
To expand on what AlephZero said, you simply need to increase your sampling time. For a signal of length NFFT, your fft will return the DFT of the signal at NFFT/2+1 discrete points ranging from 0 to fs/2. That means you just need to increase the value of NFFT in order to get more frequency bins between 0 and fs.
 
boneh3ad said:
That means you just need to increase the value of NFFT in order to get more frequency bins between 0 and fs.

We don't know what the OP's level of math education is, or anything much about the problem being solved - but "doing an FFT" is not the only way to estimate "frequency components". It's possible that it could be done much more precisely with much less data.
 
Well that's true. I assumed he was essentially looking to generate a PSD or amplitude spectrum, which I suppose is not necessarily the case.
 

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