Hilbert transform phase extraction

Compute the instantaneous phase time series for all parcels/voxels via the analytic signal (Hilbert transform). Each parcel timeseries is demeaned before transformation.

Usage

hilbert_phases(timeseries)

Arguments

timeseries

Numeric matrix [N x Tmax]. BOLD signal with N parcels as rows and Tmax timepoints as columns.

Value

Numeric matrix [N x Tmax]. Instantaneous phases in radians.

Details

All N parcels are processed in two vectorised calls to mvfft() rather than an N-iteration R loop over fft(): the timeseries matrix is transposed to a Tmax x N layout so mvfft applies the FFT to each parcel column simultaneously, the Hilbert multiplier is broadcast across columns, and the inverse FFT recovers the analytic signal for all parcels at once.

.hilbert_r() is retained as an internal single-vector reference (scipy-parity validated).

References

Cabral, J. et al. (2017). Cognitive performance in healthy older adults relates to spontaneous switching between states of functional connectivity during rest. Scientific Reports, 7(1), 5135. doi:10.1038/s41598-017-05425-7

Examples

set.seed(1)
ts <- matrix(rnorm(10 * 200), nrow = 10, ncol = 200)
phases <- hilbert_phases(ts)
dim(phases)  # 10 x 200
#> [1]  10 200