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The Propagation of Noise Fields in a Dispersive Medium

  • Leon Cohen
Chapter

Abstract

Our aim is to show how a noise field propagates in a medium that has dispersion and attenuation. For example, suppose noise with known statistical properties is generated at a particular spatial point and we ask for its statistical properties at other spatial points at a later time. We show that phase space methods are particularly effective and intuitive to study such problems. We deal with fields and stochastic processes that are not necessarily stationary either locally or globally. In the next section, we review deterministic wave propagation and we also introduce a new method for studying propagation by way of the Wigner distribution. Subsequently, we discuss the issue as to how to handle nonstationary stochastic processes using the Wigner spectrum. After these issues we address the propagation of noise fields in a dispersive deterministic medium. By a deterministic medium we mean that the medium has no random aspects and that the random aspects come in only in the initial generation of the noise field.

Keywords

White Noise Dispersion Relation Autocorrelation Function Spatial Point Spatial Spectrum 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Department of PhysicsHunter College of the City University of New YorkNew York CityUSA

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