Advertisement

Series expansions for random processes

  • L. L. Campbell
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 89)

Keywords

Spectral Density Series Expansion Random Process Reproduce Kernel Hilbert Space Sampling Theorem 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    L. L. Campbell, A series expansion for random processes, I.E.E.E. Trans. Information Theory, vol. IT-12 (1966), p. 271.Google Scholar
  2. [2]
    E. Masry, K. Steiglitz, and B. Liu, Bases in Hilbert space related to the representation of stationary operators, SIAM J. Appl. Math., vol. 16(1968), pp. 552–562.MathSciNetCrossRefzbMATHGoogle Scholar
  3. [3]
    E. Masry, B. Liu, and K. Steiglitz, Series expansion of wide-sense stationary random processes, to appear in I.E.E.E. Trans. Information Theory.Google Scholar
  4. [4]
    E. Parzen, An approach to time series analysis, Ann. Math. Statist., vol. 32 (1961), pp. 951–989.MathSciNetCrossRefzbMATHGoogle Scholar
  5. [5]
    E. Parzen, Extraction and detection problems and reproducing kernel Hilbert spaces, SIAM J. Control vol. 1 (1962), pp. 35–62.MathSciNetzbMATHGoogle Scholar
  6. [6]
    E. Parzen, Probability density functionals and reproducing kernel Hilbert spaces, in Time Series Analysis, M. Rosenblatt, editor, 1963, John Wiley and Sons, New York, pp. 155–169.Google Scholar
  7. [7]
    J. Capon, Radon Nikodym derivatives of stationary gaussian measures, Ann. Math. Statist., vol. 35 (1964), pp. 517–531.MathSciNetCrossRefzbMATHGoogle Scholar
  8. [8]
    T. Kailath, Some results on singular detection, Information and Control, vol. 9 (1966), pp. 130–152.CrossRefzbMATHGoogle Scholar
  9. [9]
    T. Kailath, A projection method for signal detection in colored Gaussian noise, I.E.E.E. Trans. Information Theory, vol. IT-13 (1967), pp 441–447.CrossRefzbMATHGoogle Scholar
  10. [10]
    N. Aronszajn, Theory of reproducing kernels, Trans. Amer. Math. Soc., vol. 68 (1950), pp. 337–404.MathSciNetCrossRefzbMATHGoogle Scholar
  11. [11]
    J. L. Doob, Stochastic Processes, John Wiley and Sons, New York, 1953.zbMATHGoogle Scholar
  12. [12]
    I. Selin, Detection Theory, Princeton University Press, Princeton, N. J., 1965.CrossRefzbMATHGoogle Scholar
  13. [13]
    E. C. Titchmarsh, Theory of Functions, 2nd ed., Oxford University Press, London 1939.zbMATHGoogle Scholar
  14. [14]
    K. Yao, Applications of reproducing kernel Hilbert spaces—bandlimited signal models, Information and Control, vol. 11 (1967), pp. 429–444.CrossRefzbMATHGoogle Scholar
  15. [15]
    W. Magnus and F. Oberhettinger, Formeln und Sätze für die speziellen Funktionen der mathematischen Physik, 2nd ed., Springer-Verlag, Berlin, 1948.CrossRefzbMATHGoogle Scholar
  16. [16]
    D. Slepian and H. O. Pollak, Prolate spheroidal wave functions, Fourier analysis and uncertainty—I, Bell System Tech, J. vol. 40 (1961), pp. 43–63.MathSciNetCrossRefzbMATHGoogle Scholar
  17. [17]
    E. J. Kelly, I. S. Reed, and W. L. Root, The detection of radar echoes in noise I, J. Soc. Indust. Appl. Math., vol. 8 (1960), pp. 309–341.MathSciNetCrossRefzbMATHGoogle Scholar
  18. [18]
    W. L. Root, Asymptotic forms of detectors of signals in noise, Mathematics Research Center, University of Wisconsin, Technical Summary Report no. 456, 1964.Google Scholar
  19. [19]
    U. Grenander and G. Szegö, Toeplitz forms and their Applications, University of California Press, Los Angeles, 1958.zbMATHGoogle Scholar
  20. [20]
    S. Kullback, Information Theory and Statistics, John Wiley and Sons, New York, 1959.zbMATHGoogle Scholar
  21. [21]
    A. Rényi, Wahrscheinlichkeitsrechnung, mit einem Anhang über Informationstheorie, Deutscher Verlag der Wissenschaften, Berlin, 1962.zbMATHGoogle Scholar
  22. [22]
    E. A. Robinson, Random Wavelets and Cybernetic Systems, Charles Griffin and Co., London, 1962.zbMATHGoogle Scholar

Copyright information

© Springer-Verlag 1969

Authors and Affiliations

  • L. L. Campbell
    • 1
  1. 1.Department of MathematicsQueen’s UniversityKingstonCanada

Personalised recommendations