Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Approximate distributions of noise power measurements

Authors: Walter Freiberger and Ulf Grenander
Journal: Quart. Appl. Math. 17 (1959), 271-283
MSC: Primary 62.00; Secondary 60.00
DOI: https://doi.org/10.1090/qam/107346
MathSciNet review: 107346
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Abstract: The frequency functions of certain spectral estimates are studied analytically and numerically. An approximation is obtained for the case of a Poisson weight function and compared to the true distribution. The eigenvalues of products of Toeplitz matrices play a crucial role in the sampling theory of quadratic forms; an approximation to their distribution is discussed and its accuracy studied numerically. This leads to approximate probability densities which are thought to be valid for moderate or even small sample sizes.

References [Enhancements On Off] (What's this?)

  • [1] Ulf Grenander and Murray Rosenblatt, Statistical analysis of stationary time series, John Wiley & Sons, New York; Almqvist & Wiksell, Stockholm, 1957. MR 0084975
  • [2] Ulf Grenander and Gabor Szegö, Toeplitz forms and their applications, California Monographs in Mathematical Sciences, University of California Press, Berkeley-Los Angeles, 1958. MR 0094840
  • [3] U. Grenander, H. O. Pollak and D. Slepian, The distribution of quadratic forms in normal variates: A small sample theory with applications to spectral analysis, (to be published)
  • [4] D. Slepian, Fluctuations of random noise power, Bell System Tech. J. 37 (1958), 163–184. MR 0092256, https://doi.org/10.1002/j.1538-7305.1958.tb03873.x
  • [5] J. J. Kalker, IBM 650 programs for matrix computations based on Jacobi's method, Brown University Rept. DA-SC-78130/1, 1958

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DOI: https://doi.org/10.1090/qam/107346
Article copyright: © Copyright 1959 American Mathematical Society

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