David M. Drumheller
David H. Hughes
Charles F. Gaumond
Acoust. Div. Naval Res. Lab., Washington, DC 20375-5350
A wavelet transform is used to synthesize distinct contributions from the monostatic form function for a randomly ribbed, complex end-capped, finite cylindrical shell. In order to achieve satisfactory wave packets, as measured by their cross-correlation with the original impulse response, two wavelet transforms are used, a temporal wavelet transform and a spectral wavelet transform. This is in contrast to synthesizing wave packets from the Wigner distribution where just one two-dimensional surface was necessary. However, interference terms between components in the Wigner distribution, which is quadratic in the underlying signal, are absent in the linear wavelet transform. This allows for a more facile synthesis of the acoustic excitations. The interference terms in the Wigner distribution can sometimes fall at points in the time-frequency plane where a signal component exists, making it difficult to synthesize that component without corruption caused by the presence of other compounds in the form function.