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