26 October 2004 Time-frequency approximation methods for driven systems
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Abstract
A method aimed at approximating the solution to differential equations with driving terms and whose solutions are non-stationary signals is described. The author has previously examined, using the approach of Galleani and Cohen the validity of the approximation method in phase space using the Wigner-distribution. He applied the method to second order differential equations and used for driving terms a variety of forcing functions that have smoothed and monotonically increasing phase functions. By examining the results, insight is gained into the nature of the solution and the associated dynamics of the system. This paper examines the approximation methods when the spectrogram is used, the spectrogram being the most widely used time-frequency distribution. The results show that the approximation scheme works very well for the spectrogram and in many cases works better than for the Wigner distribution.
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David L. Hench, "Time-frequency approximation methods for driven systems", Proc. SPIE 5559, Advanced Signal Processing Algorithms, Architectures, and Implementations XIV, (26 October 2004); doi: 10.1117/12.564251; https://doi.org/10.1117/12.564251
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