A sampling theorem for stationary (wide sense) stochastic processes.
Author:
S. P. Lloyd
Journal:
Trans. Amer. Math. Soc. 92 (1959), 112
MSC:
Primary 60.00; Secondary 94.00
MathSciNet review:
0107301
Fulltext PDF Free Access
References 
Similar Articles 
Additional Information
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E. T. Whittaker, On the functions which are represented by the expansions of the interpolationtheory, Proc. Roy. Soc. Edinburgh. Section A. vol. 35 (1915) pp. 181194.
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H. P. Kramer, A generalized sampling theorem, Bull. Amer. Math. Soc. Abstract 632234.
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Claude
E. Shannon, Communication in the presence of noise, Proc.
I.R.E. 37 (1949), 10–21. MR 0028549
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L. Doob, Stochastic processes, John Wiley & Sons, Inc.,
New York; Chapman & Hall, Limited, London, 1953. MR 0058896
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C. Oxtoby, On the ergodic theorem of Hurewicz, Ann. of Math.
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0072976 (17,361e)
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Kac, R.
Salem, and A.
Zygmund, A gap theorem, Trans. Amer. Math. Soc. 63 (1948), 235–243. MR 0023937
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S.
P. Lloyd and B.
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E. Parzen, Technical Report No. 7, Department of Statistics, Stanford University, December 22, 1956.
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A. V. Balakrishnan, A note on the sampling principle for continuous signals, Institute of Radio Engineers Transactions on Information Theory, vol. IT3 (1957) pp. 143146.
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H. Nyquist, Certain topics in telegraph transmission theory, Trans. Amer. Inst. Elec. Engrs. vol. 47 (1928) pp. 617644.
 [1]
 A.L. Cauchy, Mémoire sur diverses formulaes dé analyse, C.R. Acad. Sci. Paris vol. 12 (1841) pp. 283298.
 [2]
 E. T. Whittaker, On the functions which are represented by the expansions of the interpolationtheory, Proc. Roy. Soc. Edinburgh. Section A. vol. 35 (1915) pp. 181194.
 [3]
 H. P. Kramer, A generalized sampling theorem, Bull. Amer. Math. Soc. Abstract 632234.
 [4]
 C. E. Shannon, Communication in the presence of noise, Proc. I.R.E. vol. 37 (1949) pp. 1021. 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. 872884. 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. 221247. 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. IT3 (1957) pp. 143146.
 [12]
 H. Nyquist, Certain topics in telegraph transmission theory, Trans. Amer. Inst. Elec. Engrs. vol. 47 (1928) pp. 617644.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947195901073016
PII:
S 00029947(1959)01073016
Article copyright:
© Copyright 1959
American Mathematical Society
