Exact equations for smoothed Wigner transforms and homogenization of wave propagation

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4 Citations (Scopus)

Abstract

The Wigner transform (WT) has been extensively used in the formulation of phase-space models for a variety of wave propagation problems including high-frequency limits, nonlinear and random waves. It is well known that the WT features counterintuitive 'interference terms,' which often make computation impractical. In this connection, we propose the use of the smoothed Wigner transform (SWT), and derive new, exact equations for it, covering a broad class of wave propagation problems. Equations for spectrograms are included as a special case. The 'taming' of the interference terms by the SWT is illustrated, and an asymptotic model for the Schrödinger equation is constructed and numerically verified. © 2007 Elsevier Inc. All rights reserved.
Original languageEnglish
Pages (from-to)378-392
Number of pages15
JournalApplied and Computational Harmonic Analysis
Volume24
Issue number3
DOIs
Publication statusPublished - May 2008

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Wigner Transform
Homogenization
Wave propagation
Wave Propagation
Interference
Spectrogram
Term
Phase Space
Covering
Formulation
Model

Cite this

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title = "Exact equations for smoothed Wigner transforms and homogenization of wave propagation",
abstract = "The Wigner transform (WT) has been extensively used in the formulation of phase-space models for a variety of wave propagation problems including high-frequency limits, nonlinear and random waves. It is well known that the WT features counterintuitive 'interference terms,' which often make computation impractical. In this connection, we propose the use of the smoothed Wigner transform (SWT), and derive new, exact equations for it, covering a broad class of wave propagation problems. Equations for spectrograms are included as a special case. The 'taming' of the interference terms by the SWT is illustrated, and an asymptotic model for the Schr{\"o}dinger equation is constructed and numerically verified. {\circledC} 2007 Elsevier Inc. All rights reserved.",
author = "Athanassoulis, {Agissilaos G.}",
note = "cited By 2",
year = "2008",
month = "5",
doi = "10.1016/j.acha.2007.06.006",
language = "English",
volume = "24",
pages = "378--392",
journal = "Applied and Computational Harmonic Analysis",
issn = "1063-5203",
publisher = "Elsevier",
number = "3",

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TY - JOUR

T1 - Exact equations for smoothed Wigner transforms and homogenization of wave propagation

AU - Athanassoulis, Agissilaos G.

N1 - cited By 2

PY - 2008/5

Y1 - 2008/5

N2 - The Wigner transform (WT) has been extensively used in the formulation of phase-space models for a variety of wave propagation problems including high-frequency limits, nonlinear and random waves. It is well known that the WT features counterintuitive 'interference terms,' which often make computation impractical. In this connection, we propose the use of the smoothed Wigner transform (SWT), and derive new, exact equations for it, covering a broad class of wave propagation problems. Equations for spectrograms are included as a special case. The 'taming' of the interference terms by the SWT is illustrated, and an asymptotic model for the Schrödinger equation is constructed and numerically verified. © 2007 Elsevier Inc. All rights reserved.

AB - The Wigner transform (WT) has been extensively used in the formulation of phase-space models for a variety of wave propagation problems including high-frequency limits, nonlinear and random waves. It is well known that the WT features counterintuitive 'interference terms,' which often make computation impractical. In this connection, we propose the use of the smoothed Wigner transform (SWT), and derive new, exact equations for it, covering a broad class of wave propagation problems. Equations for spectrograms are included as a special case. The 'taming' of the interference terms by the SWT is illustrated, and an asymptotic model for the Schrödinger equation is constructed and numerically verified. © 2007 Elsevier Inc. All rights reserved.

U2 - 10.1016/j.acha.2007.06.006

DO - 10.1016/j.acha.2007.06.006

M3 - Letter

VL - 24

SP - 378

EP - 392

JO - Applied and Computational Harmonic Analysis

JF - Applied and Computational Harmonic Analysis

SN - 1063-5203

IS - 3

ER -