Why the soliton wavelet transform is useful for nonlinear dynamic phenomena

Harold H. Szu

doi:10.1117/12.138462

1 October 1992 Why the soliton wavelet transform is useful for nonlinear dynamic phenomena

Harold H. Szu

Proceedings Volume 1705, Visual Information Processing; (1992) https://doi.org/10.1117/12.138462
Event: Aerospace Sensing, 1992, Orlando, FL, United States

Abstract

If signal analyses were perfect without noise and clutters, then any transform can be equally chosen to represent the signal without any loss of information. However, if the analysis using Fourier transform (FT) happens to be a nonlinear dynamic phenomenon, the effect of nonlinearity must be postponed until a later time when a complicated mode-mode coupling is attempted without the assurance of any convergence. Alternatively, there exists a new paradigm of linear transforms called wavelet transform (WT) developed for French oil explorations. Such a WT enjoys the linear superposition principle, the computational efficiency, and the signal/noise ratio enhancement for a nonsinusoidal and nonstationary signal. Our extensions to a dynamic WT and furthermore to an adaptive WT are possible due to the fact that there exists a large set of square-integrable functions that are special solutions of the nonlinear dynamic medium and could be adopted for the WT. In order to analyze nonlinear dynamics phenomena in ocean, we are naturally led to the construction of a soliton mother wavelet. This common sense of 'pay the nonlinear price now and enjoy the linearity later' is certainly useful to probe any nonlinear dynamics. Research directions in wavelets, such as adaptivity, and neural network implementations are indicated, e.g., tailoring an active sonar profile for explorations.

Citation Download Citation

Harold H. Szu "Why the soliton wavelet transform is useful for nonlinear dynamic phenomena", Proc. SPIE 1705, Visual Information Processing, (1 October 1992); https://doi.org/10.1117/12.138462

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