Wavelet Filtering with the Mellin Transform

Details Wavelet Filtering with the Mellin Transform Wavelet Filtering with the Mellin Transform

2001-08-20

arxiv.org/abs/math-ph/0108013v1

Applied Mathematics Letters 9 #5, 1996

Physics

Mathematical Physics

8 pages in Plain Tex

Scientific paper

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 gives a one-to-one 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.

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