Accession Number : ADA307244
Title : The Mellin Transform in Signal Analysis.
Descriptive Note : Technical rept.,
Corporate Author : TEXAS UNIV AT AUSTIN APPLIED RESEARCH LABS
Personal Author(s) : Ruth, David M. ; Gilbert, John E.
PDF Url : ADA307244
Report Date : 11 MAR 1994
Pagination or Media Count : 42
Abstract : A review of the Fourier, Mellin, and Hilbert transforms is provided to lay the foundation for developing a new transform denoted the K-transform: a composition of the Fourier and Mellin transforms. In this report, the transform is defined, an explicit expression as an integral operator is derived, and an asymptotic estimate for the transform kernel is obtained. Some properties of the K-transform are explored, and the application of this transform to the work of Altes on mammalian hearing is noted. Lastly, a unified setting for Fourier and wavelet analysis is explored. The connection of the Heisenberg group with the Gabor transform and Wigner-Ville distribution is shown, as is the connection of the affine group with the wavelet transform. These notions are then combined in a single setting, the affine-Heisenberg group. In this setting, the report is closed by introducing an affine version of the Wigner-Ville distribution in terms of the K-transform.
Descriptors : *INTEGRAL TRANSFORMS, MATHEMATICAL MODELS, SIGNAL PROCESSING, FOURIER TRANSFORMATION, RESOLUTION, KERNEL FUNCTIONS, ASYMPTOTIC SERIES, CONVERGENCE, OPERATORS(MATHEMATICS), INTEGRAL EQUATIONS, TIME DOMAIN, FREQUENCY DOMAIN, MAPPING(TRANSFORMATIONS), FOURIER ANALYSIS, ANALYTIC FUNCTIONS, GROUPS(MATHEMATICS), CONVOLUTION, HYPERGEOMETRIC FUNCTIONS.
Subject Categories : Numerical Mathematics
Distribution Statement : APPROVED FOR PUBLIC RELEASE