Optimality of Natural Time Representation of Complex Time Series

TL;DR

This paper demonstrates that natural time representation optimally enhances signals in time-frequency analysis, explaining its empirical effectiveness in revealing features of complex time series.

Contribution

It provides a theoretical justification for the usefulness of natural time by showing its optimality in time-frequency signal enhancement using the Wigner function.

Findings

Natural time improves signal localization in time-frequency space.

Theoretical link between natural time and signal enhancement.

Supports empirical observations across various complex systems.

Abstract

The concept of natural time turned out to be useful in revealing dynamical features behind complex time series including electrocardiograms, ionic current fluctuations of membrane channels, seismic electric signals, and seismic event correlation. However, the origin of this empirical usefulness is yet to be clarified. Here, it is shown that this time domain is in fact optimal for enhancing the signals in time-frequency space by employing the Wigner function and measuring its localization property.