ASA 125th Meeting Ottawa 1993 May

1pNS1. Phase space engineering for mid- and high-frequency submerged structural acoustics: A wave is a wave is a wave, but what is a wavelet?

L. B. Felsen

Dept. of Elec. Eng./Weber Res. Inst., Polytechnic Univ., Six MetroTech Center, Brooklyn, NY 11201

Determining and interpreting the near and far zone mid-frequency acoustic scattering characteristics of submerged elastic structures in both the frequency and time domains requires wave-oriented spatially dependent pre- and post-signal processing. The most general framework for data analysis and synthesis is the eight-dimensional (space-time)---(wave-number-frequency) phase space that grants access by transforms and projections to various lower-dimensional subdomains that highlight distinct phenomenologies. In phase space engineering, ``wavelets'' are important basis elements for phenomenological and numerical parametrization, but there are two kinds: those usually proposed in favor of the wave aspect are smooth (analytic) compact propagators like beams or wavepackets, whereas those usually proposed in favor of the numerical processing aspect have bounded support and are generally nonsmooth. Thus, neither wavelet basis meets the demands of the other. Because scattering signatures from submerged structures have strong features driven by wave phenomenology, the processing must utilize space-wave-number portions of the phase space in addition to the conventional time frequency. Examples are shown to illustrate various wave-based parametrizations. The challenge is to construct a self-consistent hybrid scheme for phase space engineering that exploits the best of both types of wavelets. Then one can say: a wavelet is a wavelet is a wavelet. [Work supported by ONR.]