Nonlinear Signal Analysis: Time-Frequency Perspectives
Publication: Journal of Engineering Mechanics
Volume 133, Issue 2
Abstract
Recently, there has been growing utilization of time-frequency transformations for the analysis and interpretation of nonlinear and nonstationary signals in a broad spectrum of science and engineering applications. The continuous wavelet transform and empirical mode decomposition in tandem with Hilbert transform have been commonly utilized in such applications, with varying success. This study evaluates the performance of the two approaches in the analysis of a variety of classical nonlinear signals, underscoring a fundamental difference between the two approaches: the instantaneous frequency derived from the Hilbert transform characterizes subcyclic and supercyclic nonlinearities simultaneously, while wavelet-based instantaneous frequency captures supercyclic nonlinearities with a complementary measure of instantaneous bandwidth characterizing subcyclic nonlinearities. This study demonstrates that not only is the spectral content of the wavelet instantaneous bandwidth measure consistent with that of the Hilbert instantaneous frequency, but in the case of the Rössler system, produces identical oscillatory signature.
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Acknowledgments
The writers gratefully acknowledge support in part from NSF Grant No. NSFCMS 03-24331, the NASANASA Indiana Space Grant, and the Center for Applied Mathematics at the University of Notre Dame. The assistance of Ms. Lijuan Wang of the University of Notre Dame in processing the forced Duffing oscillator example is also acknowledged.
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© 2007 ASCE.
History
Received: Sep 1, 2005
Accepted: Jul 6, 2006
Published online: Feb 1, 2007
Published in print: Feb 2007
Notes
Note. Associate Editor: Raimondo Betti
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