TY - JOUR
T1 - Applications of the Generalized Morse Wavelets
T2 - A Review
AU - Erick Axel, Martinez Rios
AU - Bustamante-Bello, Rogelio
AU - Navarro-Tuch, Sergio
AU - Perez-Meana, Hector
N1 - Publisher Copyright:
© 2013 IEEE.
PY - 2023
Y1 - 2023
N2 - 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.
AB - 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.
KW - Generalized Morse wavelets
KW - applications
KW - continuous wavelet transform
KW - mother wavelet selection
KW - time-frequency analysis
UR - http://www.scopus.com/inward/record.url?scp=85146253811&partnerID=8YFLogxK
U2 - 10.1109/ACCESS.2022.3232729
DO - 10.1109/ACCESS.2022.3232729
M3 - Artículo de revisión
AN - SCOPUS:85146253811
SN - 2169-3536
VL - 11
SP - 667
EP - 688
JO - IEEE Access
JF - IEEE Access
ER -