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What is spectral_connectivity?#

spectral_connectivity is a Python software package that computes multitaper spectral estimates and frequency-domain brain connectivity measures such as coherence, spectral granger causality, and the phase lag index using the multitaper Fourier transform. Although there are other Python packages that do this (see nitime and MNE-Python), spectral_connectivity has several differences:

  • it is designed to handle multiple time series at once

  • it caches frequently computed quantities such as the cross-spectral matrix and minimum-phase-decomposition, so that connectivity measures that use the same processing steps can be more quickly computed.

  • it decouples the time-frequency transform and the connectivity measures so that if you already have a preferred way of computing Fourier coefficients (i.e. from a wavelet transform), you can use that instead.

  • it implements the non-parametric version of the spectral granger causality in Python.

  • it implements the canonical coherence, which can efficiently summarize brain-area level coherences from multielectrode recordings.

  • easier user interface for the multitaper fourier transform

  • all function are GPU-enabled if cupy is installed and the environmental variable SPECTRAL_CONNECTIVITY_ENABLE_GPU is set to ‘true’.


See the following notebooks for more information on how to use the package:

Usage Example#

from spectral_connectivity import Multitaper, Connectivity

# Compute multitaper spectral estimate
m = Multitaper(time_series=signals,

# Sets up computing connectivity measures/power from multitaper spectral estimate
c = Connectivity.from_multitaper(m)

# Here are a couple of examples
power = c.power() # spectral power
coherence = c.coherence_magnitude()
weighted_phase_lag_index = c.weighted_phase_lag_index()
canonical_coherence = c.canonical_coherence(brain_area_labels)


For citation, please use the following:

Denovellis, E.L., Myroshnychenko, M., Sarmashghi, M., and Stephen, E.P. (2022). Spectral Connectivity: a python package for computing multitaper spectral estimates and frequency-domain brain connectivity measures on the CPU and GPU. JOSS 7, 4840. 10.21105/joss.04840.

Implemented Measures#


  1. coherency

  2. canonical_coherence

  3. imaginary_coherence

  4. phase_locking_value

  5. phase_lag_index

  6. weighted_phase_lag_index

  7. debiased_squared_phase_lag_index

  8. debiased_squared_weighted_phase_lag_index

  9. pairwise_phase_consistency

  10. global coherence


  1. directed_transfer_function

  2. directed_coherence

  3. partial_directed_coherence

  4. generalized_partial_directed_coherence

  5. direct_directed_transfer_function

  6. group_delay

  7. phase_lag_index

  8. pairwise_spectral_granger_prediction

Package Dependencies#

spectral_connectivity requires:

  • python

  • numpy

  • matplotlib

  • scipy

  • xarray

See environment.yml for the most current list of dependencies.


pip install spectral_connectivity


conda install -c edeno spectral_connectivity

Developer Installation#

If you want to make contributions to this library, please use this installation.

  1. Install miniconda (or anaconda) if it isn’t already installed. Type into bash (or install from the anaconda website):

wget https://repo.continuum.io/miniconda/Miniconda3-latest-Linux-x86_64.sh -O miniconda.sh;
bash miniconda.sh -b -p $HOME/miniconda
export PATH="$HOME/miniconda/bin:$PATH"
hash -r
  1. Clone the repository to your local machine (.../spectral_connectivity) and install the anaconda environment for the repository. Type into bash:

conda env create -f environment.yml
conda activate spectral_connectivity
pip install -e .

Recent publications and pre-prints that used this software#