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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References | Similar Articles | Additional Information

**[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]**Claude E. Shannon,*Communication in the presence of noise*, Proc. I.R.E.**37**(1949), 10–21. MR**0028549****[5]**J. L. Doob,*Stochastic processes*, John Wiley & Sons, Inc., New York; Chapman & Hall, Limited, London, 1953. MR**0058896****[6]**John C. Oxtoby,*On the ergodic theorem of Hurewicz*, Ann. of Math. (2)**49**(1948), 872–884. MR**0026766**, https://doi.org/10.2307/1969403**[7]**Antoni Zygmund,*Trigonometrical series*, Dover Publications, New York, 1955. MR**0072976****[8]**M. Kac, R. Salem, and A. Zygmund,*A gap theorem*, Trans. Amer. Math. Soc.**63**(1948), 235–243. MR**0023937**, https://doi.org/10.1090/S0002-9947-1948-0023937-8**[9]**S. P. Lloyd and B. McMillan,*Linear least squares filtering and prediction of sampled signals*, Proceedings of the Symposium on Modern Network Synthesis, New York, 1955., Polytechnic Institute of Brooklyn, Brooklyn, N.Y., 1956, pp. 221–247. MR**0080406****[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