Fourier Methods in Probability

  • B. Roy Frieden
Part of the Springer Series in Information Sciences book series (SSINF, volume 10)


There is probably no aspect of probability theory that is easier to learn than its Fourier aspect. All of the linear theory [4.1] involving convolutions, Dirac delta functions, transfer theorems, and even sampling theorems has its counterparts in probability theory.


Characteristic Function Central Limit Theorem Point Spread Function Normal Curve Atmospheric Turbulence 
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Chapter 4

  1. 4.1
    R. M. Bracewell: The Fourier Transform and Its Applications (McGraw-Hill, New York 1965)MATHGoogle Scholar
  2. 4.2
    J. W. Goodman: Introduction to Fourier Optics (McGraw-Hill, New York 1968)Google Scholar
  3. 4.3
    B. R. Frieden: In Picture Processing and Digital Filtering, 2nd ed., ed. by T. S. Huang, Topics Appl. Phys., Vol. 6 (Springer, Berlin, Heidelberg, New York 1975)Google Scholar
  4. 4.4
    A. Einstein: Ann. Phys. 17,549 (1905)MATHCrossRefGoogle Scholar
  5. 4.5
    R. Barakat: Opt. Acta 21,903 (1974)MathSciNetCrossRefGoogle Scholar
  6. 4.6
    E. L. O’Neill: Introduction to Statistical Optics (Addison-Wesley, Reading, MA 1963)Google Scholar
  7. 4.7
    B. Tatian: J. Opt. Soc. Am. 55,1014 (1965)MathSciNetADSGoogle Scholar
  8. 4.8
    H. Lass: Elements of Pure and Applied Mathematics (McGraw-Hill, New York 1957)MATHGoogle Scholar
  9. 4.9
    E. Parzen: Modern Probability Theory and Its Applications (Wiley, New York 1966)Google Scholar
  10. 4.10
    A. G. Fox, T. Li: Bell Syst. Tech. J. 40,453 (1961)Google Scholar
  11. 4.11
    R. W. Lee, J. C. Harp: Proc. IEEE 57,375 (1969)CrossRefGoogle Scholar
  12. 4.12
    M. Abramowitz, I. A. Stegun (eds.): Handbook of Mathematical Functions (National Bureau of Standards, Washington, DC 1964)MATHGoogle Scholar
  13. 4.13
    J. W. Strohbehn: In Laser Beam Propagation in the Atmosphere, ed. J. W. Strohbehn, Topics in Applied Physics, Vol. 25 (Springer, Berlin, Heidelberg, New York 1978)Google Scholar

Additional Reading

  1. Araujo, A., E. Gine: The Central Limit Theorem for Real and Banach Valued Random Variables (Wiley, New York 1980)MATHGoogle Scholar
  2. Lukacs, E.: Characteristic Functions, 2nd ed. (Griffin, London 1970)MATHGoogle Scholar
  3. Moran, P. A. P.: An Introduction to Probability Theory (Clarendon, Oxford 1968)MATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1983

Authors and Affiliations

  • B. Roy Frieden
    • 1
  1. 1.Optical Sciences CenterThe University of ArizonaTucsonUSA

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