In my research area, instantaneous power in a specific frequency band is commonly estimated by the following procedure:
- Apply a bandpass filter on the raw signal (e.g. 80-90Hz bandpass).
- Estimate the analytical signal by DFT (in Matlab: hilbert())
- Take the absolute of the result.
I'm wondering how far this procedure smooths. In other words, if I perturb x(t) and then recalculate the instantaneous power, what is the most distant point that will be affected? I understand that the answer will depend on the particular bandpass filter applied. Is there an easy way to approach this?