On a Limiting Process Which Asymptotically Produces f-2 Spectral Density

  • Hirotugu Akaike
Part of the Springer Series in Statistics book series (SSS)


In the recent papers in which the results of the spectral analyses of roughnesses of runways or roadways are reported [1, 2, 3,4] the power spectral densities of approximately of the form f -2 (f: frequency) are often treated. This fact directed the present author to the investigation of the limiting process which will provide the f -2 form under fairly general assumptions. In this paper a very simple model is given which explains a way how the f -2 form is obtained asymptotically. Our fundamental model is that the stochastic process, which might be considered to represent the roughness of the runway, is obtained by alternative repetitions of roughening and smoothing. We can easily get the limiting form of the spectrum for this model. Further, by taking into account the physical meaning of roughening and smoothing we can formulate the conditions under which this general result assures that the f -2 form will eventually take place.


Power Spectrum Spectral Density Power Spectral Density Spectral Density Function Fundamental Model 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Ichiro Kaneshige, “Measurements of power spectra of roadways,” Isuzu Motor Company Technical Report 3379, 1960. (in Japanese)Google Scholar
  2. [2]
    Shun Takeda, “An investigation of airplane loads during taxiing,” Monthly Reports of Transportation Technical Research Institute. Vol. 10, No. 5, 1960. (in Japanese)Google Scholar
  3. [3]
    Wilbur E. Thompson, “Measurements and power spectra of runway roughness at airports in countries of the North Atlantic Treaty Organization,” NACA TN 4303, 1958.Google Scholar
  4. [4]
    James H. Walls, John, C. Houbolt, and Harry Press, “Some measurements and power spectra of runway roughness,” NACA TN 3305, 1954.Google Scholar

Copyright information

© Springer Science+Business Media New York 1998

Authors and Affiliations

  • Hirotugu Akaike

There are no affiliations available

Personalised recommendations