python - Improving frequency time normalization/hilbert transfer runtimes -

so bit of nitty gritty question...

i have time-series signal has non-uniform response spectrum need whiten. whitening using frequency time normalization method, incrementally filter signal between 2 frequency endpoints, using constant narrow frequency band (~1/4 lowest frequency end-member). find envelope characterizes each 1 of these narrow bands, , normalize frequency component. rebuild signal using these normalized signals... done in python (sorry, has python solution)...

here raw data:

and here spectrum:

and here spectrum of whitened data:

the problem is, have maybe ~500,000 signals this, , takes while (~a minute each)... entirety of time being spend doing actual (multiple) hilbert transforms

i have running on small cluster already. don't want parallelize loop hilbert in.

i'm looking alternative envelope routines/functions (non hilbert), or alternative ways calculate entire narrowband response function without doing loop.

the other option make frequency bands adaptive center frequency on filtering, progressively larger march through routines; decrease number of times have go through loop.

any , suggestions welcome!!!

example code/dataset: https://github.com/ashtonflinders/ftn_example

here faster method calculate enveloop local max:

def calc_envelope(x, ind):     x_abs = np.abs(x)     loc = np.where(np.diff(np.sign(np.diff(x_abs))) < 0)[0] + 1     peak = x_abs[loc]     envelope = np.interp(ind, loc, peak)     return envelope 

here example output:

it's 6x faster hilbert. speedup more, can write cython function find next local max point , normalization local max point iteratively.