Preprint: Wavelet filtering with the Mellin transform

[Gerald Kaiser (gkaiser@cs.uml.edu)]

Preprint: Wavelet filtering with the Mellin transform

Preprint: Wavelet filtering with the Mellin transform
Author: Gerald Kaiser, University of Massachusetts at Lowell

To appear in Applied Mathematics Letters

ABSTRACT: It is shown that any time-domain convolution operator can be
represented exactly as a multiplication operator in the wavelet
(time-scale) domain. The Mellin transform establishes a one-to-one
correspondence between FREQUENCY FILTERS (multipliers in frequency)
and SCALE FILTERS (multipliers in scale), subject to an ADMISSIBILITY
CONDITION requiring the convergence of the defining integrals. This
admissibility condition generalizes the usual one for the basic
wavelet, reducing to the latter when the convolution operator being
represented is the identity. Applications to the analysis and
denoising of random signals are proposed. It is argued that the
present method may be particularly useful for dealing with the effects
of atmospheric turbulence because it is ideally suited for resolving
spectral power laws.