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A sampling theorem for stationary (wide sense) stochastic processes.


Author: S. P. Lloyd
Journal: Trans. Amer. Math. Soc. 92 (1959), 1-12
MSC: Primary 60.00; Secondary 94.00
DOI: https://doi.org/10.1090/S0002-9947-1959-0107301-6
MathSciNet review: 0107301
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  • [1] A.-L. Cauchy, Mémoire sur diverses formulaes dé analyse, C.R. Acad. Sci. Paris vol. 12 (1841) pp. 283-298.
  • [2] E. T. Whittaker, On the functions which are represented by the expansions of the interpolation-theory, Proc. Roy. Soc. Edinburgh. Section A. vol. 35 (1915) pp. 181-194.
  • [3] H. P. Kramer, A generalized sampling theorem, Bull. Amer. Math. Soc. Abstract 63-2-234.
  • [4] C. E. Shannon, Communication in the presence of noise, Proc. I.R.E. vol. 37 (1949) pp. 10-21. MR 0028549 (10:464e)
  • [5] J. L. Doob, Stochastic processes, New York, Wiley, 1953. MR 0058896 (15:445b)
  • [6] J. C. Oxtoby, On the ergodic theorem of Hurewicz, Ann. of Math. vol. 49 (1948) pp. 872-884. MR 0026766 (10:199d)
  • [7] A. Zygmund, Trigonometrical series, New York, Dover, 1955 (reprint). MR 0072976 (17:361e)
  • [8] M. Kac, R. Salem and A. Zygmund, A gap theorem, Trans. Amer. Math. Soc. vol. 63 (1948) p. 235. MR 0023937 (9:426a)
  • [9] S. P. Lloyd and B. McMillan, Linear least squares filtering and prediction of sampled signals, M.R.I. Symposia Series, vol. 5, Polytechnic Institute of Brooklyn, 1956, pp. 221-247. MR 0080406 (18:242d)
  • [10] E. Parzen, Technical Report No. 7, Department of Statistics, Stanford University, December 22, 1956.
  • [11] A. V. Balakrishnan, A note on the sampling principle for continuous signals, Institute of Radio Engineers Transactions on Information Theory, vol. IT-3 (1957) pp. 143-146.
  • [12] H. Nyquist, Certain topics in telegraph transmission theory, Trans. Amer. Inst. Elec. Engrs. vol. 47 (1928) pp. 617-644.

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DOI: https://doi.org/10.1090/S0002-9947-1959-0107301-6
Article copyright: © Copyright 1959 American Mathematical Society

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