Time evolution of the wavelet transform of the acoustic field

In this paper we study the initial-value problem for a homogeneous acoustic wave equation in the two-dimensional space. Our approach is efficient if the initial data have multiscale structure and contain singularities and sharp edges. The wavelet transform is known to be a proper transform for analy...

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Bibliographic Details
Main Authors: Perel, M.V., Sidorenko, M.S., Gorodnitsky, E.A.
Format: Conference Proceeding
Language:English
Subjects:
Acoustic diffraction
Acoustic waves
Continuous wavelet transforms
Fourier transforms
Frequency
Integral equations
Partial differential equations
Physics
Wavelet analysis
Wavelet transforms
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Summary:In this paper we study the initial-value problem for a homogeneous acoustic wave equation in the two-dimensional space. Our approach is efficient if the initial data have multiscale structure and contain singularities and sharp edges. The wavelet transform is known to be a proper transform for analyzing such functions. We present a formula which describes the evolution with time of the wavelet transform of the spatial distribution of a solution. Our approach does not require an explicit calculation of the solution itself. A numerical example of the multiscale approach to the wave propagation is presented.