Imagine a filterbank with N channels. A possible implementation is a sliding short-time FFT. If you want to capture frequencies as low as 100 Hz, the length of your sliding window should be at least 10 ms. However, because of this long window length (or in general filter length), you cannot track fast temporal fluctuations in the energy at high frequencies.
Is this ever considered as a problem? How would it be adressed? A possible solution would be to different filter lengths for different channels (i.e. shorter filters for longer channels). However,
- I guess that in this case you lose the efficiency of the FFT algorithm?
- Does it even make sense to consider fast energy fluctuations at higher frequencies, while assuming that the energy in lower frequencies keeps constant?
Thanks in advance!