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Proceedings Paper

Wavelet filtering in the scale domain
Author(s): Gerald Kaiser
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Paper 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.

Paper Details

Date Published: 22 March 1996
PDF: 4 pages
Proc. SPIE 2762, Wavelet Applications III, (22 March 1996); doi: 10.1117/12.236038
Show Author Affiliations
Gerald Kaiser, Univ. of Massachusetts/Lowell (United States)

Published in SPIE Proceedings Vol. 2762:
Wavelet Applications III
Harold H. Szu, Editor(s)

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