syncopy.specest.mtmconvol.mtmconvol#

syncopy.specest.mtmconvol.mtmconvol(data_arr, samplerate, nperseg, noverlap=None, taper='hann', taper_opt=None, boundary='zeros', padded=True, detrend=False)[source]#

(Multi-)tapered short time 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

  • nperseg (int) – Sliding window size in sample units

  • noverlap (int) – Overlap between consecutive windows, set to nperseg - 1 to cover the whole signal

  • 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

  • boundary (str or None) – Wether or not to auto-pad the signal such that a window is centered on each sample. If set to None half the window size (nperseg) will be lost on each side of the signal. Defaults ‘zeros’, for zero padding extension.

  • padded (bool) – Additional padding in case noverlap != nperseg - 1 to fit an integer number of windows.

Returns:

  • ftr (4D numpy.ndarray) – The Fourier transforms, complex output has shape: (nTime, 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 STFT result is normalized such that this yields the power spectral density. For a clean harmonic and a frequency bin width of dF this will give a peak power of A**2 / 2 * dF, with A as harmonic ampltiude.