def _calc_inst_phase(self, sig, alpha):
"""Extract analytical signal through the Hilbert Transform."""
analytic_signal = hilbert(sig) # Apply Hilbert transform to each row
if alpha is not None:
assert -0.5 < alpha < 0.5 , '`alpha` must be in between -0.5 and 0.5'
real_part = np.array([filt6(row.real, alpha) for row in analytic_signal])
imag_part = np.array([filt6(row.imag, alpha) for row in analytic_signal])
analytic_signal = real_part + 1j*imag_part
phase = np.unwrap(np.angle(analytic_signal)) # Compute angle between img and real
if alpha is not None:
phase = np.array([filt6(row, alpha) for row in phase]) # Filter phase
return phase
def _calc_inst_freq(self, sig, t, order, alpha):
"""Extracts instantaneous frequency through the Hilbert Transform."""
inst_phase = self._calc_inst_phase(sig, alpha=alpha)
if order is False:
inst_freqs = np.diff(inst_phase)/(2*np.pi*(t[1]-t[0]))
inst_freqs = np.concatenate((inst_freqs,
inst_freqs[:,-1].reshape(inst_freqs[:,-1].shape[0],1)), axis=1)
else:
inst_freqs = [pade6(row, t[1]-t[0])/(2.0*np.pi) for row in inst_phase]
if alpha is None:
return np.array(inst_freqs)
else:
return np.array([filt6(row, alpha) for row in inst_freqs]) # Filter freqs