Application of wavelets to scattering for wave‐packet synthesis

The wavelet transform can be used to analyze the time‐scale domain structure of echoes derived from broadband, monostatic, acoustic scattering from ribbed shells. In the time‐scale domain, the echoes can be seen to be composed primarily of a few individual components. Each component corresponds to a separate physical scattering mechanism in the shell. Yen has called these separated components wave packets, each having distinctive time‐scale dimensions that derive from the physical process that generates it. Because each wave packet has distinctive time‐scale domain properties and the wavelet transform is invertible, the wavelet transform can be used to isolate and synthesize a set of wave packets. The resulting wave packets are functions of aspect and time. Greater efficiency of representation can be achieved by representing these wave packets with a bilinear expansion. Wave packets generated with the wavelet transform can be used for matched filter detection. [Work supported by the Office of Naval Research.]