A Python signal processing package for computing spectral- and time-domain interactions using the bispectrum.

This package provides the tools for computing phase-amplitude coupling, time delay estimation, and wave shape features using the bispectrum and bicoherence. Additional tools for computing amplitude-amplitude coupling, phase-phase coupling, and spatio-spectral filters are also provided.

Parallel processing and Numba optimisation are implemented to reduce computation times.

Analysis of phase-amplitude coupling, time delays, and non-sinusoidal waveshape provide important insights into electrophysiology data, but traditional analysis methods have critical limitations. In contrast, the bispectrum - the Fourier transform of the third order moment - offers approaches to perform such analyses whilst overcoming many of the limitations of traditional methods.

Installation & Requirements:

Install the package into the desired environment using pip: pip install pybispectra
or conda: conda install -c conda-forge pybispectra
More information on the installation page.

Use:

To get started with the toolbox, check out the documentation and examples.

For instance, given some epoched time series, data, phase-amplitude coupling can be computed as:

frompybispectraimportPAC, compute_fftcoeffs, freqs=compute_fft(data, sampling_freq) # compute spectral coeffspac=PAC(coeffs, freqs, sampling_freq) # initialise coupling objectpac.compute() # compute phase-amplitude couplingpac_results=pac.results# extract resultspac_results.plot() # plot results

Contributing & Development:

If you encounter issues with the package, want to suggest improvements, or have made any changes which you would like to see officially supported, please refer to the development page. A unit test suite is included and must be expanded where necessary to validate any changes.

Citing:

If you use this toolbox in your work, please include the following citation:
Binns, TS, Pellegrini, F, Jurhar, T, Nguyen, TD, Köhler, RM, & Haufe, S (2025). PyBispectra: A toolbox for advanced electrophysiological signal processing using the bispectrum. Journal of Open Source Software. DOI: 10.21105/joss.08504