def slidingFFT( se, T , n = 1 , tStart = None , preSample = False , nHarmo = 5 , kind = abs , phase = None) :
"""
Harmonic analysis on a sliding windows
se : Series to analyse
T : Period
tStart : start _xAxis
n : size of the sliding windows in period.
reSample : reSample the signal so that a period correspond to a integer number of time step
nHarmo : number of harmonics to return
kind : module, real, imaginary part, as a function (abs, np.imag, np.real ...)
phase : phase shift (for instance to extract in-phase with cos or sin)
"""
if (type(se) == pd.DataFrame) :
if len(se.columns) == 1 : se = se.iloc[:,0]
nWin = int(0.5 + n*T / dx(se) )
#ReSample to get round number of time step per period
if preSample :
new = reSample( se, dt = n*T / (nWin) )
else :
new = se
signal = new.values[:]
#Allocate results
res = np.zeros( (new.shape[0] , nHarmo ) )
for iWin in range(new.shape[0] - nWin) :
sig = signal[ iWin : iWin+nWin ] #windows
fft = np.fft.fft( sig ) #FTT
if phase !=None : #Phase shift
fft *= np.exp( 1j* ( 2*pi*(iWin*1./nWin) + phase ))
fftp = kind( fft ) #Take module, real or imaginary part
spectre = 2*fftp/(nWin) #Scale
for ih in range(nHarmo):
res[iWin, ih] = spectre[ih*n]
if ih == 0 : res[iWin, ih] /= 2.0
#if ih == 0 : res[iWin, ih] = 2.0
return pd.DataFrame( data = res , index = new.index , columns = map( lambda x : "Harmo {:} ({:})".format(x , se.name ) , range(nHarmo) ) )
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