neurotools.signal.morlet module

Coherence measures based on the Morlet wavelength.

This allows adjusting the spectral and temporal nfreqss depending on frequency.

neurotools.signal.morlet.normalized_morlet(m, w)[source]

See morlet(m,w)

This applies post-processing such that the sum absolute magnitued of the wavelet is 1

neurotools.signal.morlet.prepare_wavelet_fft_basis(fa, fb, nfreqs, L, w, Fs=1000)[source]
Parameters:

  • fa (positive float) – Low-frequency cutoff in Hz

  • fb (positive float) – High-frequency cutoff in Hz

  • nfreqs (positive int) – Specral sampling nfreqs

  • L (positive int) – Number of samples

  • w (float) – Base frequency, passed as second argument to morlet()

  • Fs (positive int; default 1000) – Sampling rate

Returns:

  • freqs – FFT frequencies

  • basis – Fourier transform of Morlet wavelets for each band.

neurotools.signal.morlet.fft_cwt(data, fa, fb, w=4.0, nfreqs=0.1, Fs=1000)[source]

Wavelet transform.

Parameters:

  • data – NTIMES × NCHANNELS np.array

  • w (positive float; default 4.0) – Wavelet base frequency; Controls the time-frequency tradeoff

  • nfreqs (positive float; default 0.1) – Frequency sampling nfreqs

  • Fs (positive int; default 1000) – Sample rate

Returns:

  • freqs – Frequencies of each band, in Hz

  • result (NCHANNELS × NFREQS × NTIMES np.array) – wavelet transform

neurotools.signal.morlet.geometric_window(c, w)[source]

Gemoetrically centered frequency window.

Parameters:

  • c (float) – Center of frequency window

  • w (float) – width of frequency window

Returns:

  • fa (float) – low-frequency cutoff

  • fb (float) – high-frequency cutoff

neurotools.signal.morlet.logfreqs(fa, fb, nfreq)[source]
Parameters:

  • fa (positive float) – Low-frequency cutoff in Hz

  • fb (positive float) – High-frequency cutoff in Hz

  • nfreq (positive int) – Number of frequency bands

Returns:

freqs – list of logarithmically-spaced frequencies between fa and fb.

Return type:

np.array

neurotools.signal.morlet.prepare_wavelet_fft_basis_logspace(fa, fb, nfreq, L, w, Fs=1000)[source]
Parameters:

  • fa (positive float) – Low-frequency cutoff in Hz

  • fb (positive float) – High-frequency cutoff in Hz

  • nfreq (positive int) – Number of frequency bands

  • L (positive int) – Number of samples

  • w (float) – Base frequency, passed as second argument to morlet()

  • Fs (positive int; default 1000) – Sampling rate

Returns:

  • freqs – FFT frequencies

  • basis – Fourier transform of Morlet wavelets for each band.

neurotools.signal.morlet.population_synchrony_spectrum(lfp, fa, fb, w=4.0, nfreqs=0.1, Fs=1000)[source]

Use Morlet wavelets to compute short-timescale synchrony.

Parameters:

  • lfp (np.array) – First dimension is nchannels, second is time.

  • w (positive float; default 4.0) – Wavelet base frequency; Controls the time-frequency tradeoff

  • nfreqs (positive float; default 0.1) – Frequency sampling nfreqs

  • Fs (positive int; default 1000) – Sample rate

Returns:

  • freqs (NFREQS np.array) – Frequencies of each band, in Hz

  • synchrony – NCHANNELS × NFREQS × NTIMES np.array

neurotools.signal.morlet.fft_cwt_transposed(data, fa, fb, w=4.0, nfreqs=1000, Fs=1000.0, threads=1)[source]

Compute morelet spectrogam of a list of time-domain signals (possibly in parallel if you have a threaded installation of the FFTW library available).

This version spaces nfreqs frquencies uniformly between fa and fb, inclusive. For logarithmic spacing, see fft_cwt_transposed_logspaced().

Parameters:

  • data (numeric) – NCH x Ntimes list of signals to transform

  • fa (float) – Lowest frequency to extract

  • fb (float) – Highest frequency to extract

  • 4 (float; default 4.0) – Time/frequency morlet width parameter

  • nfreqs (int; default 1000) – Number of frequency components to use

  • Fs (float; default 1000.0) – Sample rate in Hz

  • threads (int; default 1) – Number of threads to use

Returns:

  • freqs (float) – frequencies

  • result (wavelt transforms) – Nch x Nfreq x Ntimes

neurotools.signal.morlet.fft_cwt_transposed_logspaced(data, fa, fb, w=4.0, nfreqs=None, Fs=1000.0, threads=1)[source]

Compute morelet spectrogam of a list of time-domain signals (possibly in parallel if you have a threaded installation of the FFTW library available).

This version spaces nfreqs frquencies logarithmically between fa and fb, inclusive. For uniform spacing, see fft_cwt_transposed().

Parameters:

  • data (NCHANNELS × NTIMES np.array)

  • fa (positive float) – Low-frequency cutoff in Hz

  • fb (positive float) – High-frequency cutoff in Hz

  • w (positive float; default 4.0) – Wavelet base frequency; Controls the time-frequency tradeoff

  • nfreqs (positive float; default 0.1) – Frequency sampling nfreqs

  • Fs (positive int; default 1000) – Sample rate

  • threads (positive int; default 1) – Number of CPU threads to use

Returns:

  • freqs – Frequencies of each band, in Hz

  • result (NCHANNELS × NFREQS × NTIMES np.array) – wavelet transform

neurotools.signal.morlet.convenient_morlet(N, f0, sigma_ms, Fs)[source]
neurotools.signal.morlet.get_gentle_morlets_ft(N, flo=2, f0=15, fhi=45, sigma_lo=166.66666666666666, sigma_md=100, nfreqs=100, Fs=1000)[source]
neurotools.signal.morlet.gentle_morlet_psd(u, flo=2, f0=15, fhi=45, sigma_lo=166.66666666666666, sigma_md=100, nfreqs=100, Fs=1000)[source]
Returns:

psd – NFREQS x NSAMPLES power spectrum

Return type:

np.ndarray