Wavelet Filtering with the Mellin Transform
Abstract
It is shown that any convolution operator in the time domain can be represented exactly as a multiplication operator in the timescale (wavelet) domain. The Mellin transform gives a onetoone correspondence between frequency filters (multiplications in the frequency domain) and scale filters (multiplications in the scale domain), subject to the convergence of the defining integrals. The usual wavelet reconstruction theorem is a special case. Applications to the denoising of random signals are proposed. It is argued that the present method is more suitable for removing the effects of atmospheric turbulence than the conventional procedures because it is ideally suited for resolving spectral power laws.
 Publication:

arXiv eprints
 Pub Date:
 August 2001
 arXiv:
 arXiv:mathph/0108013
 Bibcode:
 2001math.ph...8013K
 Keywords:

 Mathematical Physics;
 Functional Analysis;
 44XX;
 41XX
 EPrint:
 8 pages in Plain Tex