Garner C. Bishop
Naval Undersea Warfare Ctr. Div. Newport, Newport, RI 02840
A null field T-matrix formalism for plane-wave scattering from a doubly infinite fluid--solid interface with doubly periodic surface roughness [Bishop and Smith, J. Acoust. Soc. Am. 94, 1560--1583 (1993)] is extended to include scattering of broadband acoustic pulses. The scattered pressure field is expressed in terms of a Fourier integral over the spectra of the incident pulse and the T matrix. Time series are calculated for the scatter of a Gaussian amplitude-modulated linear frequency-modulated pulse from a fluid--elastic interface with sinusoidal and triangular roughness. The time series are analyzed using short time Fourier, Wigner, wavelet packet, and local cosine T-F transforms. The results are displayed graphically in a T-F plot in which the T-F plane is covered by rectangular boxes of dimensions (Delta)tx(Delta)(omega). These results are used to evaluate the ability of each of the transforms to address inverse scattering and identification problems. It is shown that the T-F analysis provided by the wavelet packet may be used to distinguish between the scatter from surfaces of different roughness and is superior to the T-F analysis provided by both the short time Fourier and Wigner transforms.