Applications of the Generalized Morse Wavelets: A Review

Abstract

The study of signals, processes, and systems has motivated the development of different representations that can be used to analyze and understand them. Classical ways of studying the behavior of signals are the time domain and frequency domain representations. For the analysis of non-stationary signals, time-frequency representations have become an essential tool to understand how the frequency content of signals changes with time. A common time-frequency technique employed in the literature is the wavelet transform. Nevertheless, selecting an adequate mother wavelet to perform the wavelet transform has become challenging due to the diverse available wavelet families. This paper reviews the applications and uses of a particular class of wavelet basis known as the Generalized Morse Wavelets. This class of wavelet family provides a systematic framework to choose and generate a wavelet for general-purpose use. This study reviews the application of Generalized Morse Wavelets in biomedical engineering, dynamical systems analysis, electrical engineering, geophysics, and communication systems. Moreover, the parameters of the Generalized Morse Wavelets used in each study are presented. The results of this study reveal that Generalized Morse Wavelets have proven helpful in studying signals, systems, and processes in areas ranging from biomedical engineering to geophysics. Nonetheless, the parameters of the Generalized Morse Wavelets are yet to be chosen through a rigorous methodology and argumentation. Therefore, there is an opportunity to generate methods for selecting the parameters of the Generalized Morse Wavelets based on the characteristics of the signals, systems, or processes under research.INDEX TERMS Generalized Morse wavelets, mother wavelet selection, continuous wavelet transform, applications, time-frequency analysis.

Ground Fault in Medium-Voltage Power Networks with an Isolated Neutral Point: Spectral and Wavelet Analysis of Selected Cases in an Example Industrial Network Modeled in the ATP-EMTP Package

“…By inserting the α value described by Formula (25) and the ω 1 and ω 2 values described by Formulas ( 18) and ( 19) into the solution (38) and (39), we obtain, after some transformations,…”

“…The wavelet transform, on the other hand, is based on functions with a rapidly decaying (time-constrained) support and therefore allows a much more accurate analysis of the variation in the individual components of the relay protection criterion signal. Hence, in order to delve deeper into the electromagnetic transient processes described here, a continuous wavelet transform based on analytical Morse wavelets [37,38] was used in our case study. The continuous wavelet transform makes it possible to watch the fluctuation of the individual components over shorter periods of time.…”