syncopy.specest.mtmfft.mtmfft#

syncopy.specest.mtmfft.mtmfft(data_arr, samplerate, nSamples=None, taper='hann', taper_opt=None, demean_taper=False, ft_compat=False)[source]#

(Multi-)tapered fast Fourier transform. Returns full complex Fourier transform for each taper. Multi-tapering only supported with Slepian windwows (taper=”dpss”).

Parameters:

  • data_arr ((N,) numpy.ndarray) – Uniformly sampled multi-channel time-series data The 1st dimension is interpreted as the time axis

  • samplerate (float) – Samplerate in Hz

  • nSamples (int or None) – Absolute length of the (potentially to be padded) signals or None for no padding.

  • taper (str or None) – Taper function to use, one of scipy.signal.windows Set to None for no tapering.

  • taper_opt (dict or None) – Additional keyword arguments passed to the taper function. For multi-tapering with taper='dpss' set the keys ‘Kmax’ and ‘NW’. For further details, please refer to the SciPy docs

  • demean_taper (bool) – Set to True to perform de-meaning after tapering

  • ft_compat (bool) – Set to True to use Field Trip’s normalization, which is NOT independent of the padding size

Returns:

  • ftr (3D numpy.ndarray) – Complex output has shape (nTapers x nFreq x nChannels).

  • freqs (1D numpy.ndarray) – Array of Fourier frequencies

Notes

For a (MTM) power spectral estimate average the absolute squared transforms across tapers:

Sxx = np.real(ftr * ftr.conj()).mean(axis=0)

The FFT result is normalized such that this yields the spectral power. For a clean harmonic this will give a peak power of A**2 / 2, with A as harmonic amplitude.