Research on the unified mathematical model for FT, STFT and WT and its applications

This paper presents and discusses a unified mathematical model for some classical signal transforms. The study not only gives theoretical insights in signal transforms, but also provides application values. The mathematical models of Fourier transform (FT), short time Fourier transform (STFT) and wa...

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Bibliographic Details
Published in:Mechanical systems and signal processing 2004-11, Vol.18 (6), p.1335-1347
Main Authors: Qin, S.R., Zhong, Y.M.
Format: Article
Language:English
Subjects:
Application
Signal transforms
Unified mathematical model
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Summary:This paper presents and discusses a unified mathematical model for some classical signal transforms. The study not only gives theoretical insights in signal transforms, but also provides application values. The mathematical models of Fourier transform (FT), short time Fourier transform (STFT) and wavelet transform (WT) are studied, and the general form of the unified model of these three transforms are derived. The flow charts of these models are presented and discussed. The specific values of the variables and parameter functions of FT, STFT and WT in unified mathematical model are given. Finally, some examples are presented to show the applications of the unified mathematical models of signal transforms.
ISSN:0888-3270
1096-1216
DOI:10.1016/j.ymssp.2003.12.002