Phase Entropy

Computes the phase entropy (PhasEn) of a one-dimensional signal (Rohila & Sharma, 2019) from its Second-Order Difference Plot (SODP). Each point plots the first difference \(x(n+\tau)-x(n)\) against the second difference \(x(n+2\tau)-x(n+\tau)\); the polar angle of each point is binned into \(k\) equal sectors of \([0, 2\pi)\), and PhasEn is the (normalized) Shannon entropy of the angle-weighted sector distribution. It summarizes how the signal's local rate-of-change and its change-of-rate co-vary – a phase-plane geometry distinct from the amplitude, template-matching and symbolic (dispersion/increment/slope) entropies.

Usage

phaseEntropy(x, delay = 1L, k = 4L)

Arguments

x: A numeric vector (the time series).
delay: Time delay (lag) in samples for the differences (default 1).
k: Number of angular sectors of the SODP (default 4).

Value

A single numeric value, the phase entropy.

Details

This implementation reproduces NeuroKit2's entropy_phase bit-for-bit, including its normalization (a base-2 Shannon term divided by the natural-log \(\ln k\), so PhasEn ranges in \([0, 1/\ln 2]\)).

References

Rohila, A., & Sharma, A. (2019). "Phase entropy: a new complexity measure for heart rate variability." Physiological Measurement, 40(10), 105006. doi:10.1088/1361-6579/ab499e

Examples

set.seed(1)
phaseEntropy(rnorm(1000), k = 4)
#> [1] 1.154952