Analysis and separation of time-frequency components in signals with chaotic behavior

TL;DR

This paper introduces two novel time-frequency transformations using linear and hyperbolic chirps to analyze and separate chaotic components in signals, demonstrated through plasma reflectometry and stochastic processes.

Contribution

The paper presents new orthogonal transformations based on linear and hyperbolic chirps for analyzing chaotic signals, linking them to existing methods.

Findings

Linear chirp transformation effectively isolates chaotic components in non-stationary signals.

Hyperbolic chirp transformation detects chaotic parts in self-similar stochastic processes.

Mathematical connections established with existing time-frequency methods.

Abstract

The analysis of chaotic signals with time-frequency methods is considered. For this purpose, two new transformations are presented which consist in the decomposition of a signal onto an orthogonal set of respectively linear and hyperbolic chirps. The linear chirp transformation is able to discriminate and extract particular chaotic components in non-stationary square integrable signals. This is demonstrated in an example studying the reflectometry measures of a turbulent plasma. The hyperbolic chirp transformation is designed for the detection and extraction of chaotic parts in self-similar processes such as stochastic motions. Mathematical connections are made between these two methods and other well-known transformations.