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.