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I understand that the Hilbert transform on broadband data produces uninterpretable results. And so we first bandpass the data, and then run the Hilbert transform.

My question is, how wide can the band be before the data starts to become meaningless? Is it just a matter of degree, or does the method suddenly cease to work at a certain bandwidth? Does it matter if the frequencies are high or low?

For my purposes, I would like to filter time series data at 2-12 Hz, and then run the Hilbert transform to extract phase and power information. Is this narrow enough of a band?

Edit: my sampling rate is 1000. I don't really have requirements on filter order but have been using a length 2000 filter. My time series data are tens of thousands of samples long. The frequency range of the broadband time series data is 0-120.

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    $\begingroup$ Not enough information. If you have an infinitely long filter whose amplitude can go to infinity at $\omega = 0$, and infinite precision, then there are no limits on the bandwidth of the input data. Please edit your question to tell us what length filter can you stand, what is your sampling rate, and do you have any constraints on precision? $\endgroup$ – TimWescott Nov 21 '19 at 18:23
  • $\begingroup$ If you "understand that the Hilbert transform on broadband data produces uninterpretable results", then you are my liege $\endgroup$ – Laurent Duval Nov 21 '19 at 23:59
  • $\begingroup$ What's the lowest frequency at which you want to maintain accuracy? That pretty much directly limits the length of the filter, with lower frequencies and higher accuracies needing longer filters. $\endgroup$ – TimWescott Nov 22 '19 at 0:41
  • $\begingroup$ Well my bandpass filter is currently 2-12 Hz. So let's say I'd like to maintain accuracy at 2Hz. That would be the lowest frequency at which I'd want to maintain accuracy. $\endgroup$ – amd1972 Nov 22 '19 at 2:23
  • $\begingroup$ Bump. Please advise! Thank you $\endgroup$ – amd1972 Nov 24 '19 at 22:23

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