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Dissertation
Sinusoidal time-frequency wavelets
Doctor of Philosophy (Ph.D.), Drexel University
1998
DOI:
https://doi.org/10.17918/00010330
Abstract
Windowed Fourier transform provides us with a true time-frequency localization analysis yet can not overcome the resolution limitation imposed by the scale of the selected window function to zoom into the time-frequency details of the signal. Wavelet transform utilizes all scales of the signal and can zoom into time-frequency details, with properly selected mother wavelet, for time-frequency localization. Not all wavelets have sinusoidal oscillating patterns needed for signal frequency analysis. We present the sinusoidal wavelets of both real sine and complex exponential oscillating patterns to take full advantage of Fourier frequency analysis and wavelet scale analysis. The sinusoidal wavelet family is designed to provide us with a true time-frequency analysis, instead of time-scale analysis, for time-frequency localization of both stationary and non-stationary signals. We present general expressions for the sinusoidal wavelet family with various window functions and show that all these sinusoidal wavelets meet the wavelet admissibility condition. We also evaluate the time-frequency localization characteristics of the sinusoidal wavelet family. We simulate the time-frequency localization performance of some commonly used time-scale wavelets and the sinusoidal time-frequency wavelets. We show that not all time-scale wavelets are suitable for time-frequency localization and that the sinusoidal wavelets as a family is a much better alternative, by design, to time-scale wavelets for time-frequency feature analysis. We show that the sinusoidal wavelet family offers convenient trade-off adjustment between time resolution at low frequencies and frequency resolution at high frequencies for any given time-frequency analysis application. We also present the complex exponential wavelets which separate the time translation modulus information and the time translation phase information and can thus be applied to provide a better visual representation of the time-frequency analysis. We show that the modulated Gaussian wavelet is a special case of our complex exponential Gaussian wavelet. We apply the sinusoidal wavelets to time-frequency analysis of recordings of electrogastrographic (EGG) signals provided to us by University of Rochester and University of Oklahoma and demonstrate that our sinusoidal wavelets can simultaneously localize high frequency spike activities and track low frequency slow waves of the electrogastrographic signals.
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Details
- Title
- Sinusoidal time-frequency wavelets
- Creators
- Xiang Xie
- Contributors
- Hun Hsuan Sun (Advisor) - Drexel University, Drexel University (1970-)
- Awarding Institution
- Drexel University
- Degree Awarded
- Doctor of Philosophy (Ph.D.)
- Publisher
- Drexel University; Philadelphia, Pennsylvania
- Number of pages
- xxi, 295 pages
- Resource Type
- Dissertation
- Language
- English
- Academic Unit
- College of Engineering (1970-2026); Drexel University
- Other Identifier
- 991021888939604721