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Tytuł artykułu

Modes and Noise Propagation in Phase Space

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
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.
Słowa kluczowe
Wydawca
Czasopismo
Rocznik
Tom
2
Numer
1
Opis fizyczny
Daty
otrzymano
2014-09-11
zaakceptowano
2015-05-12
online
2015-12-24
Twórcy
  • City University of New York, 695
    Park Ave. New York, NY 10065 USA
autor
  • City University of New York, 695
    Park Ave. New York, NY 10065 USA
Bibliografia
  • [1] J. S. Ben-Benjamin and L. Cohen, “Pulse propagation and windowedwave functions", J. of Modern Optics, 61, 36-42, 2014
  • [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.
  • [7] L. Cohen, The Weyl Operator and its Generalization, Birkhauser,2013.
  • [8] L. Cohen, “Time-Frequency Distributions - A Review,” Proc. ofthe IEEE, vol. 77, pp. 941-981, 1989.
  • [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.
  • [18] M. D. Greenberg, Foundations of AppliedMathematics, PrenticeHall, 1978.
  • [19] J. D. Jackson, Classical Electrodynamics, Wiley, 1992.
  • [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.
  • [25] W. D. Mark, “Spectral Analysis of the Convolution and Filteringof Non-Stationary Stochastic Processes”, Jour. Sound Vibration,11, pp. 19-63, 1970.
  • [26] W.Martin, “Time-Frequency Analysis of Random. Signals", Proc.ICASSP 82, pp. 1325-1328,. 1982.
  • [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.
  • [31] W.P. Schleich, Quantum Optics in Phase Space, Wiley, 2001.
  • [32] I. Tolstoy and C. Clay, Ocean Acoustics: Theory and Experimentin Underwater Sound, AIP, NY 1987.
  • [33] G. Whitham, Linear and Nonlinear Waves, J. Wiley and Sons,New York, 1974.
  • [34] E. P. Wigner, “On the quantum correction for thermodynamicequilibrium,” Physical Review, 40, 749–759, 1932.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.-psjd-doi-10_1515_coph-2015-0003
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