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Description II: Spectral Density

  • John D. Robson
  • Colin J. Dodds
  • Donald B. Macvean
  • Vincent R. Paling
Part of the International Centre for Mechanical Sciences book series (CISM, volume 115)

Abstract

The probability functions which we have considered give an account of the part played in a random process by values of x of different magnitudes, but they do not reveal the course of the variation of x with time except through the auto-correlation function R(τ) as a function of time interval τ. We are accustomed in vibration work to think of time variation as measured rather by frequency, and we now consider how we can apply this concept to a random function, through the method of Fourier analysis. We shall find that this leads us back to the auto-correlation function by a different path.

Keywords

Spectral Density Fourier Series Random Process Random Function Basic Frequency 
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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Bibliography for Chapter 3

  1. 3.1
    Lawden D.F.: Mathematics of Engineering Systems: Methuen 1959 (also paperback). This applies the theory to random processes.Google Scholar
  2. 3.2.
    Kaplan W.: Operational Methods for Linear Systems: Addison—Wesley 1962. More advanced in treatment, but does not touch random processes.MATHGoogle Scholar

Copyright information

© Springer-Verlag Wien 1971

Authors and Affiliations

  • John D. Robson
    • 1
    • 2
  • Colin J. Dodds
    • 1
  • Donald B. Macvean
    • 1
  • Vincent R. Paling
    • 1
  1. 1.University of GlasgowUK
  2. 2.UdineItaly

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