BiSPy : Bivariate Signal Processing with Python

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BiSPy is an open-source python framework for processing bivariate signals. It supports our papers on time-frequency analysis [1], spectral analysis [2] and linear time-invariant filtering [3] of bivariate signals.

[1] Julien Flamant, Nicolas Le Bihan, Pierre Chainais: “Time-frequency analysis of bivariate signals”, In press, Applied and Computational Harmonic Analysis, 2017; arXiv:1609.0246, doi:10.1016/j.acha.2017.05.007

[2] Julien Flamant, Nicolas Le Bihan, Pierre Chainais: “Spectral analysis of stationary random bivariate signals”, 2017, IEEE Transactions on Signal Processing; arXiv:1703.06417, doi:10.1109/TSP.2017.2736494

[3] Julien Flamant, Pierre Chainais, Nicolas Le Bihan: “A complete framework for linear filtering of bivariate signals”, 2018; Accepted for publication in IEEE Transactions on Signal Processing; arXiv:1802.02469

These papers contains theoretical results and several applications that can be reproduced with this toolbox.

This python toolbox is currently under development and is hosted on GitHub. If you encounter a bug or something unexpected please let me know by raising an issue on the project page.


BiSPy works with python 3.5+.


To install dependencies:

pip install numpy scipy matplotlib numpy-quaternion

quaternion add quaternion dtype support to numpy. Implementation by [moble]. Since this python toolbox relies extensively on this module, you can check out first the nice introduction here.

Install from sources

Clone this repository

git clone
cd bispy

And execute

pip install .


This software is distributed under the CeCILL Free Software Licence Agreement

Cite this work

If you use this package for your own work, please consider citing it with this piece of BibTeX:

    title =   {{BiSPy: an Open-Source Python project for processing bivariate signals}},
    author =  {Julien Flamant},
    year =    {2018},
    url =     {},
    howpublished = {Online at: \url{}},
    note =    {Code at, documentation at}