### ASA 126th Meeting Denver 1993 October 4-8

## 3pPA2. Decomposition of scattered waves from an isolated elastic object
with time-frequency representation.

**Nai-chyuan Yen
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*Phys. Acoust. Branch, Naval Res. Lab., Washington, DC 20375-5320
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In observing the scattering phenomena from an isolated elastic object, one
would like to understand the composition of the scattered waves so the
characteristic structure of the scatterer can be estimated. This paper reviews
such an inverse scattering problem in terms of wave packet decomposition.
Particularly, the focus is on a heuristic approach that has been developed from
the study of acoustic scattering. The basic scheme of this approach is to
examine the coherence property of the wave signature of the scattered waves and
to compute its energy distribution in a joint time and frequency
representation. Also shown is how to apply signal synthesis techniques to
determine the dominant components, namely wave packets, expressed as the
natural frame (basis), the building block for the formulation of the scattered
wave. The magnitude and the phase of each wave packet are evaluated by
algorithms that treat them as the independent nonorthogonal components from a
set of linear equations. Examples of the response of the scattered waves from
shell type elastic objects are used to illustrate the physical implication of
this decomposition method in resolving the inverse scattering problem. It is
concluded that the wave packet decomposition by means of the natural frame
(basis) can be considered as a generalized Gabor and/or wavelet transform.
Their relationships are discussed through the fundamentals of linear functional
analysis.