Entropy-Based Concentration and Instantaneous Frequency of TFDs from Cohen’s, Affine, and Reassigned Classes

Abstract

This paper explores three groups of time–frequency distributions: the Cohen’s, affine, and reassigned classes of time–frequency representations (TFRs). This study provides detailed insight into the theory behind the selected TFRs belonging to these classes. Extensive numerical simulations were performed with examples that illustrate the behavior of the analyzed TFR classes in the joint time–frequency domain. The methods were applied both on synthetic and real-life non-stationary signals. The obtained results were assessed with respect to time–frequency concentration (measured by the Rényi entropy), instantaneous frequency (IF) estimation accuracy, cross-term presence in the TFRs, and the computational cost of the TFRs. This study gives valuable insight into the advantages and limitations of the analyzed TFRs and assists in selecting the proper distribution when analyzing given non-stationary signals in the time–frequency domain.

Optimising Time-Frequency Distributions: A Surface Metrology Approach

“…Time-frequency representations result from various time-frequency distributions and are methods of describing temporal variations of signals' spectral content [1]. In general, there are linear, quadratic and higher-order classes of distributions with applications investigated in diverse fields of research, such as instantaneous frequency estimation [2][3][4][5][6], parameter determination [7][8][9], signal modelling [10][11][12], wireless resource management [13,14], target localisation [15][16][17], and biomedical signal abnormalities [18][19][20][21][22][23]. Time-frequency representations augment and extend the classical analysis by offering additional features that can help better discriminate and classify diverse phenomena, and this is paramount for emerging pattern recognition and machine learning applications [24].…”

Signal Processing and Machine Learning for Smart Sensing Applications

“…Bačnar et al [ 12 ] elaborated on and compares three classes of time-frequency representations (TFRs): Cohen’s, affine, and reassigned, including the theoretical background of the selected TFRs belonging to these classes. Next, the authors performed extensive numerical simulations on non-stationary signals, including both synthetic and real-life examples.…”