Signal Analysis in Chaotic Systems: A Comprehensive Assessment through Time-Frequency Analysis

Abstract

Non-stationary and nonlinear signals, which can bring important applications in chaotic dynamics, and are found in several scientific and engineering fields. Several processing techniques have been used to understand and extract information from these signals, and the literature shows that time-frequency analysis techniques are suitable tools for this characterization. They allow to examine the time-varying characteristics of the signals. In this chapter, we will explore time-frequency methods applied especially to nonlinear signals. First, we discuss the diverse range of dynamical systems. Then, we introduce the classical time-frequency methods, including the Short-Time Fourier Transform, the Wavelet Transform, the Hilbert Transform, and the Wigner-Ville distribution. These methods have been widely used in the literature in the study of non-stationary operations. Thus, we present emerging methods of time-frequency analysis, taking advantage of post-processing and synchrosqueezing techniques to improve the accuracy and resolution of the time-frequency representation. We present a comprehensive analysis of these emerging methods, comparing them with classical approaches to show their contributions. Our main goal is to highlight the capabilities of these emerging time-frequency analysis methods in capturing and understanding chaotic patterns in signals.