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Mellin Convolution for Signal Filtering and Its Application to the Gaussianization of Lévy Noise

[+] Author Affiliations
Gianni Pagnini

CRS4, Pula, CA, Italy

YangQuan Chen

Utah State University, Logan, UT

Paper No. DETC2011-47392, pp. 149-154; 6 pages
doi:10.1115/DETC2011-47392
From:
  • ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 3: 2011 ASME/IEEE International Conference on Mechatronic and Embedded Systems and Applications, Parts A and B
  • Washington, DC, USA, August 28–31, 2011
  • Conference Sponsors: Design Engineering Division and Computers and Information in Engineering Division
  • ISBN: 978-0-7918-5480-8
  • Copyright © 2011 by ASME

abstract

Noises are usually assumed to be Gaussian so that many existing signal processing techniques can be applied with no worry. However, in many real world natural or man-made systems, noises are usually heavy-tailed. It is increasingly desirable to address the problem of finding an opportune filter function for a given input noise in order to generate a desired output noise. By filtering theory, the probability density function of the output noise can be expressed by the integral of the product of the density of the input noise and the filter function. Adopting Mellin transformation rules, the Mellin transform of the unknown filter is determined by the Mellin transforms of the known density of the input noise and the desired density for the output noise. Finally, after the inversion, the Mellin-Barnes integral representation of the filter function is derived. The method is applied to compute the filter function to convert a Levy noise into a Gaussian noise.

Copyright © 2011 by ASME

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