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

[jollage]

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?

 

[analogdesign]

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.

 

[sophiecentaur]

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.

 

[sophiecentaur]

An additional thing; your Nyquist anti-aliasing filter can be very non critical in its high frequency performance.

 

[AlephZero]

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.

 

[boneh3ad]

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 f_s/2. That means you just need to increase the value of NFFT in order to get more frequency bins between 0 and f_s.

 

[AlephZero]

That means you just need to increase the value of NFFT in order to get more frequency bins between 0 and f_s.

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.

 

[boneh3ad]

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.