Summary

Plugin name : Connectivity Measure
Version : 0.0.1
Author : Arthur DESBOIS
Company : Inria
Short description : Connectivity Measure
Documentation template generation date : Apr 20 2022

Description

Measure connectivity between pairs of channel

This box measure connectivity between all channels of a signal using several method. For now, Coherence, Magnitude Squared Coherence, Imaginary part of Coherence, and absolute value of the Imaginary part are available.
They are defined in [1].

The coherence definitions used are :

\[ Coherence = \frac{\left| S_{xy} \right|}{sqrt{(P_{xx}.P_{yy})} } \]

\[ Magnitude Squared Coherence = \frac{\left| S_{xy} \right|^2}{(P_{xx}.P_{yy})} \]

\[ Imaginary Coherence = \frac{Im(S_{xy})}{sqrt{(P_{xx}.P_{yy})} } \]

\[ Absolute Value Of Imaginary Coherence = \frac{\left| Im(S_{xy}) \right|}{sqrt{(P_{xx}.P_{yy})} } \]

With \( S_{xy} \) the cross-spectral density between two signal channels, and \( P_{xx} \) and \( P_{yy} \) the Power Spectral Densities of the two channels.
The spectral densities are estimated via Welch's method [2]

[1] Nolte & al (2004) "Identifying true brain interaction from EEG data using the imaginary part of coherency", Clinical Neurophysiology Volume 115, Issue 10, October 2004

[2] Welch, P.D. (1967) "The Use of Fast Fourier Transform for the Estimation of Power Spectra: A Method Based on Time Averaging Over Short, Modified Periodograms", IEEE Transactions on Audio Electroacoustics, AU-15, 70–73

Inputs

1. Input signal

The input signal on which connectivity between channels will be measured.

Type identifier : Signal (0x5ba36127, 0x195feae1)

Outputs

The output of the box is the connectivity Matrix

1. Connectivity Matrix

The connectivity matrix is a 3D Matrix of size frequency_taps x nb_channels x nb_channels

Type identifier : Streamed matrix (0x544a003e, 0x6dcba5f6)

Settings

1. Metric

Choice of the algorithm to measure the connectivity (Magnitude Squared Coherence, Imaginary Coherence).

Type identifier : Metric method (0x9188339d, 0x5da83a84)
Default value : [ Coherence ]

2. Welch Window method

The windowing method to apply. Available options are Hamming, Hanning and Welch.

Type identifier : Welch Window method (0x8815bfa7, 0x557b102f)
Default value : [ Hann ]

3. Welch Window Length (in sec)

The length of the window in seconds for the windowing method.

Type identifier : Float (0x512a166f, 0x5c3ef83f)
Default value : [ 0.25 ]

4. Welch Window Overlap (in %)

The percentage of overlap of the windowing method

Type identifier : Integer (0x007deef9, 0x2f3e95c6)
Default value : [ 50 ]

5. Connectivity Measure Length (in sec)

The length of signal to receive (in seconds) before processing the connectivity on it.

Type identifier : Float (0x512a166f, 0x5c3ef83f)
Default value : [ 0.5 ]

6. Connectivity Measure Overlap (in %)

The percentage of signal overlap to process the connectivity on.

Type identifier : Integer (0x007deef9, 0x2f3e95c6)
Default value : [ 50 ]

7. FFT size (frequency taps)

The amount of frequency taps for the connectivity measure.

Type identifier : Integer (0x007deef9, 0x2f3e95c6)
Default value : [ 128 ]

8. DC removal

Option to remove DC component from signal.

Type identifier : Boolean (0x2cdb2f0b, 0x12f231ea)
Default value : [ false ]