Wave packet decomposition

Various decomposition techniques have been employed in signal processing for exploiting and highlighting the characteristics of a given signal. The approach discussed in this paper, conceived from the observation of wave packets in scattering phenomena, is to examine the natural representation of a signal through the dynamic time and frequency properties of its energy distribution. For a time-varying signal from a physical system with finite energy content, the selected natural frame component functions, which may not be necessarily orthogonal, can form a complete set for the particular signal under analysis. The decomposition with these nonorthogonal frames then becomes optimal and unique. Algorithms for evaluating the composition of this type of frame are derived from the coherence property of the given signal and image processing is used to estimate the approximate form of needed functions. A simulated multimode signal and the response of the scattered wave signature from an isolated spherical shell are examples used to illustrate a heuristic approach, based on this decomposition method, for resolving the inverse problem in physical systems.