48 lines
2.3 KiB
Python
48 lines
2.3 KiB
Python
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import numpy as np
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def multipleFilterAnalysis(data,alfa,cfreq,dt,ndec):
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"""
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Perform a multiple filter analysis of data.
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data: Array of detrended and demeaned data whose length is power of 2
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alfa: Width parameter of Gaussian bandpass filter
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cfreq: Array of center frequencies of Gaussian filter
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dt: sampling interval of data
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ndec: decimation factor for instantaneous amplitude output
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"""
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npts = len(data)
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nd = int(pow(2, np.ceil(np.log(npts)/np.log(2)))) # find next higher power of 2 of npts
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ftd = np.fft.rfft(data,nd) # Fourier transform of entire data set (pos. freq.)
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# data are padded with zeros since npts <= nd
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freq = np.fft.rfftfreq(nd,dt) # Fourier frequencies (positive frequencies)
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nt = int(np.ceil(npts/ndec))
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mfa = np.zeros((len(cfreq),nt)) # numpy array for MFA result
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for jf,cf in enumerate(cfreq):
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hg = np.exp(-alfa*((freq-cf)/cf)**2) # Gaussian filter (use f instead of omega here)
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fk = hg*ftd # multiply FT of data with filter
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qk = np.complex(0,1)*fk # FT of Hilbert transform
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ftk = np.fft.irfft(fk) # filtered data
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qtk = np.fft.irfft(qk) # Hilbert transform of filtered data
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at = np.sqrt(ftk**2+qtk**2) # instantaneous amplitude
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mfa[jf,:] = at[0:npts:ndec] # store decimated original result
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return mfa
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#-----------------------------------------------------------------------
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# normalize multiple filter result either along time or frequency axis
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def normalizeMFT(mfa,mode,exp):
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"""
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Normalize the result of the mutiple filtering operation.
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mfa: array with instantaneous amplitudes versus frequency (mfa(f,t))
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mode: normalization mode: if 'time', normalize along time axis
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else normalize along frequency axis
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exp: exponent for modifying inst amp using a power less than 1
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"""
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nf,nt = mfa.shape
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if mode == 'time':
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for jf in range(0,nf):
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mfamax = np.amax(mfa[jf,:])
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mfa[jf,:] = np.power(mfa[jf,:]/mfamax+1.e-10,exp)
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else:
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for jt in range(0,nt):
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mfamax = np.amax(mfa[:,jt])
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mfa[:,jt] = np.power(mfa[:,jt]/mfamax+1.e-10,exp)
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return mfa
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