Estimating a phase for a frequency band

I'm looking for a way (preferably already implemented in eg. python) of estimating a phase for a specified freq band.

When I'm performing FFT on the signal, I can determine components frequencies as well as phases of interesting components. If I understand this well, a single complex number in the FFT result table is, in fact, a representation of some (small and determined by the sampling rate and length of signal) freq band. But what if I want specific a frequency band on my own? Eg. I want to estimate a phase (single number) for a frequency band of 9-11 Hz. I guess even it's possible, some information will be lost. But can I do that?

• Phase needs a reference. What time (or other reference point) do you consider to be zero phase? Without that, phase of a signal is meaningless. Dec 14 '20 at 20:32

Not really. The DFT is first and foremost a mathematical procedure that simply allows representing a time domain sequence as a sum of complex exponentials. The physical interpretation of that operation depends a lot on the circumstances but in general it's NOT true that FFT coefficient at some frequency $$\omega$$ represents accurately what's happening physically at frequency $$\omega$$. They are related but the exact nature of the relationship depends a lot on the details.