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2014 | 2 | 1 |

Article title

Modes and Noise Propagation in Phase Space

Content

Title variants

Languages of publication

EN

Abstracts

EN
We show that phase space methods developed
for quantum mechanics, such as the Wigner distribution,
can be effectively used to study the evolution of nonstationary
noise in dispersive media. We formulate the issue
in terms of modes and show how modes evolve and
how they are effected by sources.We show that each mode
satisfies a Schrödinger type equation where the “Hamiltonian”
may not be Hermitian. The Hamiltonian operator
corresponds to dispersion relationwhere thewavenumber
is replaced by the wavenumber operator. A complex dispersion
relation corresponds to a non Hermitian operator
and indicates that we have attenuation. A number of examples
are given.

Keywords

Publisher

Year

Volume

2

Issue

1

Physical description

Dates

received
11 - 9 - 2014
accepted
12 - 5 - 2015
online
24 - 12 - 2015

Contributors

  • City University of New York, 695
    Park Ave. New York, NY 10065 USA
author
  • City University of New York, 695
    Park Ave. New York, NY 10065 USA

References

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  • [2] J. S. Ben-Benjamin and L. Cohen “Propagation in channels”,SPIE vol. 8744, 874413-1:874413-16, 2013 .
  • [3] J. S. Ben-Benjamin and L. Cohen,“Nonstationary noise propagationwith sources”, Proc. SPIE 9090, Automatic Target RecognitionXXIV, 909007, 2014 (doi: 10.1117/12.2053113).
  • [4] J. S. Ben-Benjamin and L. Cohen, “The Effect of Sources onModes”, to be submitted.
  • [5] L. Cohen, “Generalized phase–space distribution functions,”Jour. Math. Phys., vol. 7, pp. 781–786, 1966.
  • [6] L. Cohen, Time-Frequency Analysis, Prentice-Hall, 1995.
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  • [9] L. Cohen, “Phase-Space Differential Equations for Modes”, OperatorTheory: Advances and Applications, vol. 205, pp. 235-250, 2009.
  • [10] L. Cohen, “The History of Noise”, IEEE Signal Processing Magazine,Volume 22, Issue 6, 20 - 45, 2005.
  • [11] P. Faure, “Theoretical Model of Reverberation Noise”, J. Acoust.Soc. Am., Vol. 36, 259-266, 1964.
  • [12] L. Galleani and L. Cohen, “TheWigner distribution for classicalsystems,” Physics Letters A, vol. 302, pp. 149-155, 2002.
  • [13] L. Galleani and L. Cohen, “The phase space of nonstationarynoise”, Journal of Modern Optics, vol. 51, pp. 2731-2740, 2004.
  • [14] L. Galleani and L. Cohen, “Time-frequency characterization ofrandom systems," Proc. SPIE, vol. 5205, 2003.
  • [15] L. Galleani and L. Cohen, “Wigner Distribution for Random Systems”J. Mod. Optics, 49, 2657-2665 2003.
  • [16] L. Galleani and L. Cohen,“Nonstationary stochastic differentialequations”, in: Advances of nonlinear signal and image processing,S. Marshall and G. Sicuranza (Eds.), Hindowi Publishing,pp. 1-13, 2006.
  • [17] K. Graff, Wave Motion in Elastic Solids, Oxford University Press,1975.
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  • [20] H.W. Lee, “Theory and application of quantumphase-space distributionfunctions”, Physics Reports, 259, 147-211, 1995.
  • [21] P. Loughlin and L. Cohen, “Phase-space approach to wave propagationwith dispersion and damping," Proc. SPIE, vol. 5559, p.221-231, 2004. 1268-1271, 2005.
  • [22] P. Loughlin and L. Cohen, “A Wigner approximation method forwave propagation,” J. Acoust. Soc. Amer., vol. 118, no. 3, pp.1268-1271, 2005.
  • [23] P. Loughlin and L. Cohen, “Approximate wave function from approximatenon-representable Wigner distributions,” J. ModernOptics, vol. 55, no. 19/20, pp. 3379-3387, 2008
  • [24] P. Loughlin and L. Cohen, “Local properties of dispersivepulses,” J. Mod. Optics, vol. 49, no. 14/15, pp. 2645-2655, 2002.
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  • [27] W. Martin and P. Flandrin, “Wigner–Ville spectral analysis ofnonstationary processes,” IEEE Trans. Acoust. Speech, SignalProcess. 33, 1461–1470 (1985).
  • [28] D. Middleton, “A statistical theory of reverberation and similarfirst-order scattered fields”, Parts I and II, IEEE Transactions onInformation Theory, vol. IT-13, 372-392 and 393-414, 1967; “Astatistical theory of reverberation and similar first-order scatteredfields”, Parts III and IV, IEEE Transactions on InformationTheory, vol. IT-18, 35-67 and 68-90, 1972.
  • [29] P. H. Morse and K. U. Ingard, Theoretical Acoustics, McGraw-Hill1968.
  • [30] V. V. Ol’shveskii, Characteristics of Sea Reverberation, ConsultantsBureau, 1967.
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  • [34] E. P. Wigner, “On the quantum correction for thermodynamicequilibrium,” Physical Review, 40, 749–759, 1932.

Document Type

Publication order reference

Identifiers

YADDA identifier

bwmeta1.element.-psjd-doi-10_1515_coph-2015-0003
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