smvgc_to_mvgc
Average (integrate) frequency-domain causality over specified frequency range
Syntax
F = smvgc_to_mvgc(f,B)
Arguments
See also Common variable names and data structures.
input
f spectral (frequency-domain) Granger causality
B frequency range; if unspecified (default) entire frequency
range is used
_output_F Granger causality (time domain)
Description
Calculates (conditional or unconditional) time-domain causality F from spectral causality f by integration (numerical quadrature - see quads) over the frequency range B. If a frequency band B is not supplied (default), the spectral causality is averaged from zero to the Nyqvist frequency. In that case the formula
(see [1]), where 
is the Nyqvist frequency, should hold (at least approximately, numerically; see e.g. mvgc_demo).
A frequency band B is specified by a vector comprising pairs of points in ascending order in the range [0,1] - corresponding to zero up to the Nyqvist frequency. See quadsr for more details. In this case band-limited time-domain causality [1,2] is calculated.
References
[1] L. Barnett and A. K. Seth, The MVGC Multivariate Granger Causality Toolbox: A New Approach to Granger-causal Inference, J. Neurosci. Methods 223, 2014 [ preprint ].
[2] L. Barnett and A. K. Seth, "Behaviour of Granger causality under filtering: Theoretical invariance and practical application", J. Neurosci. Methods 201(2), 2011.