Multidimensional wave field signal theory: transfer function relationships
type: Item
instance of: scholarly article
title: Multidimensional wave field signal theory: transfer function relationships
zbMATH Open document ID: 1264.94038
DOI: 10.1155/2012/478295
author: N. Baddour
published in: Mathematical Problems in Engineering
publication date: 2013-06-11T00:00:00Z
review text: Summary: The transmission of information by propagating or diffusive waves is common to many fields of engineering and physics. Such physical phenomena are governed by a Helmholtz (real wavenumber) or pseudo-Helmholtz (complex wavenumber) equation. Since these equations are linear, it would be useful to be able to use tools from signal theory in solving related problems. The aim of this paper is to derive multidimensional input/output transfer function relationships in the spatial domain for these equations in order to permit such a signal theoretic approach to problem solving. This paper presents such transfer function relationships for the spatial (not Fourier) domain within appropriate coordinate systems. It is shown that the relationships assume particularly simple and computationally useful forms once the appropriate curvilinear version of a multidimensional spatial Fourier transform is used. These results are shown for both real and complex wavenumbers. Fourier inversion of these formulas would have applications for tomographic problems in various modalities. In the case of real wavenumbers, these inversion formulas are presented in closed form, whereby an input can be calculated from a given or measured wavefield.
Mathematics Subject Classification ID: 94A12
zbMATH DE Number: 6173314
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/478295
OpenAlex ID: W2005740289
Wikidata QID: Q58911749
cites work: Q2734598
cites work: Q3996223
cites work: Image-enhanced thermal-wave slice diffraction tomography with numerically simulated reconstructions
cites work: Thermal-wave infrared radiometric slice diffraction tomography with back-scattering and transmission reconstructions: experimental
cites work: Thermal-wave slice tomography using wave-field reconstruction
cites work: A multi-dimensional transfer function approach to photo-acoustic signal analysis
cites work: Fourier diffraction theorem for diffusion-based thermal tomography
cites work: Q3986025
cites work: Algebraic Signal Processing Theory: Cooley–Tukey Type Algorithms for DCTs and DSTs
cites work: Algebraic Signal Processing Theory: Foundation and 1-D Time
cites work: Algebraic Signal Processing Theory: 1-D Space
cites work: Algebraic signal processing theory: Cooley-Tukey type algorithms on the 2-D hexagonal spatial lattice
cites work: An operational calculus for the Euclidean motion group with applications in robotics and polymer science
cites work: Q4330500
cites work: Gaussian quadrature formulas for the numerica l integration of Bromwich's integral and the inversion of the Laplace transform
cites work: Computing Fourier transforms and convolutions on the 2-sphere
cites work: Q5558293
Recommended article: Representation of two-dimensional wave fields by multidimensional signals
Recommended article: Wavelet multipliers and signals
Recommended article: Q3992274
Recommended article: Multidimensional transfer function models
Recommended article: The transfer function and the frequency response of a multidimensional continuous-pulse system
Recommended article: Q4977400
Recommended article: Multiwavelet analysis and signal processing
Recommended article: Q4026784
Recommended article: Q4845298
Recommended article: Multidimensional models for analysing frequency modulated signals
description: scientific article; zbMATH DE number 6173314