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Wavelet Transform Application for/in Non-Stationary Time-Series Analysis: A Review

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Laboratoire RIADI, Ecole Nationale des Sciences de l’Informatique, la Manouba 2010, Tunisia
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Centre d’applications et de Recherches en Télédétection (CARTEL), Université de Sherbrooke, Sherbrooke, QC J1K 2R1, Canada
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Laboratoire ITI Department, IMT Atlantique, 29238 Brest-Iroise, France
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Departament de Física de la Terra i Termodinàmica, Universitat de Valencia, Burjassot, 46100 València, Spain
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Laboratory of Water Cycle and Related Land Surface Processes, Institute of Geographic Sciences and Natural Resources Research, Chinese Academy of Sciences, Beijing 100101, China
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Authors to whom correspondence should be addressed.
Appl. Sci. 2019, 9(7), 1345; https://doi.org/10.3390/app9071345
Received: 2 March 2019 / Revised: 20 March 2019 / Accepted: 26 March 2019 / Published: 30 March 2019
(This article belongs to the Section Applied Physics)
Non-stationary time series (TS) analysis has gained an explosive interest over the recent decades in different applied sciences. In fact, several decomposition methods were developed in order to extract various components (e.g., seasonal, trend and abrupt components) from the non-stationary TS, which allows for an improved interpretation of the temporal variability. The wavelet transform (WT) has been successfully applied over an extraordinary range of fields in order to decompose the non-stationary TS into time-frequency domain. For this reason, the WT method is briefly introduced and reviewed in this paper. In addition, this latter includes different research and applications of the WT to non-stationary TS in seven different applied sciences fields, namely the geo-sciences and geophysics, remote sensing in vegetation analysis, engineering, hydrology, finance, medicine, and other fields, such as ecology, renewable energy, chemistry and history. Finally, five challenges and future works, such as the selection of the type of wavelet, selection of the adequate mother wavelet, selection of the scale, the combination between wavelet transform and machine learning algorithm and the interpretation of the obtained components, are also discussed. View Full-Text
Keywords: wavelet transform; non stationary; time series; time-frequency; decomposition; applied sciences wavelet transform; non stationary; time series; time-frequency; decomposition; applied sciences
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MDPI and ACS Style

Rhif, M.; Ben Abbes, A.; Farah, I.R.; Martínez, B.; Sang, Y. Wavelet Transform Application for/in Non-Stationary Time-Series Analysis: A Review. Appl. Sci. 2019, 9, 1345.

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