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Proceedings Paper

Time-frequency representations applied to canonical Newtonian gradient forms: I
Author(s): David H. Hughes
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Paper Abstract

Canonical polynomial forms taken from Thom's cuspoid family of catastrophes are studied as anharmonic oscillator potentials via time-frequency representations. Polynomial coefficients are control parameters, allowed to vary with time, inducing sudden changes in instantaneous equilibrium positions as well as characteristic oscillations about those equilibria that exhibit slowly varying spectra. Higher order potentials organize lower order potentials, which are contained in the higher order potentials, resulting in similar time-frequency signatures of the Newtonian dynamics ensuing as the potential changes with time.

Paper Details

Date Published: 8 March 2002
PDF: 9 pages
Proc. SPIE 4738, Wavelet and Independent Component Analysis Applications IX, (8 March 2002); doi: 10.1117/12.458749
Show Author Affiliations
David H. Hughes, Air Force Research Lab. (United States)

Published in SPIE Proceedings Vol. 4738:
Wavelet and Independent Component Analysis Applications IX
Harold H. Szu; James R. Buss, Editor(s)

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