Wavelet filtering in the scale domain

Gerald Kaiser

doi:10.1117/12.236038

22 March 1996 Wavelet filtering in the scale domain

Gerald Kaiser

Proceedings Volume 2762, Wavelet Applications III; (1996) https://doi.org/10.1117/12.236038
Event: Aerospace/Defense Sensing and Controls, 1996, Orlando, FL, United States

Abstract

It is shown that any convolution operator in the time domain can be represented exactly as a multiplication operator in the time-scale (wavelet) domain. The Mellin transform establishes a one-to-one correspondence between frequency filters (system or transfer functions) and scale filters, which are defined as multiplication operators in the scale domain, subject to the convergence of the defining integrals. Applications to the denoising of random signals are proposed. We argue that the present method is more suitable for removing the effects of atmospheric turbulence than the conventional procedures based on Fourier analysis because it is ideally suited for resolving spectral power laws.

Citation Download Citation

Gerald Kaiser "Wavelet filtering in the scale domain", Proc. SPIE 2762, Wavelet Applications III, (22 March 1996); https://doi.org/10.1117/12.236038

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