Applications of the Generalized Morse Wavelets: A Review
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 sig...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
IEEE
2023-01-01
|
| Series: | IEEE Access |
| Subjects: | |
| Online Access: | https://ieeexplore.ieee.org/document/9999638/ |
| _version_ | 1797946363103674368 |
|---|---|
| author | Erick Axel Martinez-Rios Rogelio Bustamante-Bello Sergio Navarro-Tuch Hector Perez-Meana |
| author_facet | Erick Axel Martinez-Rios Rogelio Bustamante-Bello Sergio Navarro-Tuch Hector Perez-Meana |
| author_sort | Erick Axel Martinez-Rios |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-10T21:09:49Z |
| format | Article |
| id | doaj.art-5ba65606048e44f684679f9eb67dc686 |
| institution | Directory Open Access Journal |
| issn | 2169-3536 |
| language | English |
| last_indexed | 2024-04-10T21:09:49Z |
| publishDate | 2023-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj.art-5ba65606048e44f684679f9eb67dc6862023-01-21T00:00:51ZengIEEEIEEE Access2169-35362023-01-011166768810.1109/ACCESS.2022.32327299999638Applications of the Generalized Morse Wavelets: A ReviewErick Axel Martinez-Rios0https://orcid.org/0000-0003-0918-366XRogelio Bustamante-Bello1https://orcid.org/0000-0001-9270-0052Sergio Navarro-Tuch2Hector Perez-Meana3School of Engineering and Sciences, Tecnologico de Monterrey, Mexico City, MexicoSchool of Engineering and Sciences, Tecnologico de Monterrey, Mexico City, MexicoSchool of Engineering and Sciences, Tecnologico de Monterrey, Mexico City, MexicoESIME Culhuacan, Instituto Politecnico Nacional, Mexico City, MexicoThe 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.https://ieeexplore.ieee.org/document/9999638/Generalized Morse waveletsmother wavelet selectioncontinuous wavelet transformapplicationstime-frequency analysis |
| spellingShingle | Erick Axel Martinez-Rios Rogelio Bustamante-Bello Sergio Navarro-Tuch Hector Perez-Meana Applications of the Generalized Morse Wavelets: A Review IEEE Access Generalized Morse wavelets mother wavelet selection continuous wavelet transform applications time-frequency analysis |
| title | Applications of the Generalized Morse Wavelets: A Review |
| title_full | Applications of the Generalized Morse Wavelets: A Review |
| title_fullStr | Applications of the Generalized Morse Wavelets: A Review |
| title_full_unstemmed | Applications of the Generalized Morse Wavelets: A Review |
| title_short | Applications of the Generalized Morse Wavelets: A Review |
| title_sort | applications of the generalized morse wavelets a review |
| topic | Generalized Morse wavelets mother wavelet selection continuous wavelet transform applications time-frequency analysis |
| url | https://ieeexplore.ieee.org/document/9999638/ |
| work_keys_str_mv | AT erickaxelmartinezrios applicationsofthegeneralizedmorsewaveletsareview AT rogeliobustamantebello applicationsofthegeneralizedmorsewaveletsareview AT sergionavarrotuch applicationsofthegeneralizedmorsewaveletsareview AT hectorperezmeana applicationsofthegeneralizedmorsewaveletsareview |