Covariance equivalent forms and evolutionary spectra for nonstationary random processes

  • J. K. Hammond
  • R. F. Harrison
Session 1 Non Stationary Processes
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 62)


Many nonstationary random processes exhibit a "frequency modulated" structure. In this paper a method of modelling such processes as the output of a time variable filter driven by white noise is described. The basis of the method relies on producing a process that is "covariance equivalent" to the process under consideration. This particular formulation makes it possible to predict the evolutionary (time-frequency) spectral density of the process.

The theoretical basis of the method is explained and this is followed by a detailed example which illustrates the theory. The example is concerned with the prediction of the evolutionary spectral density of the motion of a vehicle accelerating over rough terrain. The terrain is described as a spatially homogeneous random process and the nonstationarity of the response arises because of the variable velocity of the vehicle.

The covariance equivalent formulation is quite general and other applications (which include problems in acoustics) are noted.


State Transition Matrix Nonstationary Process Rough Terrain Shaping Filter Evolutionary Spectrum 
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7. References

  1. 1.
    M.B. PRIESTLEY 1965 J.R. Stat. Soc. B27. Evolutionary spectra and nonstationary processes.Google Scholar
  2. 2.
    M.B. PRIESTLEY 1966 J.R. Stat. Soc. B28. Design relations for nonstationary processes.Google Scholar
  3. 3.
    L. ZADEH 1950 Proc. IRE, 38. Frequency analysis of variable networks.Google Scholar
  4. 4.
    J.K. HAMMOND, Y.H. TSAO and R.F. HARRISON 1983 Proc. ICASSP, Boston. Evolutionary spectral density models having a frequency modulated structure.Google Scholar
  5. 5.
    R.F. HARRISON 1983 Ph.D. Thesis, ISVR, University of Southampton, England, The nonstationary response of vehicles on rough ground.Google Scholar
  6. 6.
    Y.H. TSAO 1983 Ph.D. Thesis, ISVR, University of Southampton, England. Frequency-time methods in acoustics.Google Scholar

Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • J. K. Hammond
    • 1
  • R. F. Harrison
    • 1
  1. 1.Institute of Sound and Vibration ResearchUniversity of SouthamptonEngland

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