The Mellin-Parseval formula and its interconnections with the exponential sampling theorem of optical physics

被引：22

作者：

Bardaro, Carlo ^{[1
]}

Butzer, Paul L. ^{[2
]}

Mantellini, Ilaria ^{[1
]}

机构：

[1] Univ Perugia, Dept Math & Comp Sci, I-06123 Perugia, Italy

[2] Rhein Westfal TH Aachen, Lehrstuhl Math, D-52056 Aachen, Germany

来源：

INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS | 2016年 / 27卷 / 01期

关键词：

Mellin transform; Mellin bandlimited functions; exponential sampling theorem; reproducing kernel formula; Mellin-Parseval formula; APPROXIMATION; CONVERGENCE; OPERATORS;

D O I：

10.1080/10652469.2015.1087401

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we establish a Mellin version of the classical Parseval formula of Fourier analysis in the case of Mellin bandlimited functions, and its equivalence with the exponential sampling formula (ESF)of signal analysis, in which the samples are not equally spaced apart as in the classical Shannon theorem, but exponentially spaced. Two quite different examples are given illustrating the truncation error in the ESF. We employ Mellin transform methods for square-integrable functions.

引用

页码：17 / 29

页数：13

共 3 条

[1] The sampling theorem, Poisson's summation formula, general Parseval formula, reproducing kernel formula and the Paley-Wiener theorem for bandlimited signals - their interconnections
Butzer, P. L.
Ferreira, P. J. S. G.
Higgins, J. R.
Schmeisser, G.
Stens, R. L.
[J]. APPLICABLE ANALYSIS, 2011, 90 (3-4) : 431 - 461
[2] The Exponential Sampling Theorem of Signal Analysis and the Reproducing Kernel Formula in the Mellin Transform Setting
Carlo Bardaro
Paul Leo Butzer
Ilaria Mantellini
[J]. Sampling Theory in Signal and Image Processing, 2014, 13 (1): : 35 - 66
[3] AN AXIAL FORM IN SAMPLING THEOREM AND ITS APPLICATION TO OPTICAL DIFFRACTION
ARSENAULT, H
BOIVIN, A
[J]. JOURNAL OF APPLIED PHYSICS, 1967, 38 (10) : 3988 - +

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