Sampling Reconstruction of Stochastic Signals– The Roots in the Fifties
DOI:
https://doi.org/10.17713/ajs.v36i1.321Abstract
In this article we are interested in the beginnings and the development of the sampling theory in signal analysis of stochastic signals, locating these in the early fifties. Besides the most important papers by Parzen (1956), Balakrishnan (1957), Belyaev (1959), and Lloyd (1959) we expose and report on few other interesting articles not widely known, giving an overview of the topic.References
Balakrishnan, A. V. (1957). A note on the sampling principle for continous signals. IRE Trans. Information Theory(IT-3), 143-146.
Belyaev, Y. K. (1959). Analytical random processes. Teor. Veroyatnost. i Primenen, 4, 437-444. (Russian)
Beutler, F. E. (1961). Sampling theorems and bases in a Hilbert space. Information and Control, 4, 97-117.
Kotel’nikov, V. A. (1933). On the capacity of the ”ether” and wire in radio communication, in materials of the 1st ussr congr. techn. reconstruction in communication eng. and developm. weak current industry. USSR Energy Committe, Moscow.
Lloyd, S. P. (1959). A sampling theorem for stationary (wide sense) stochastic processes. Trans. Amer. Math. Soc., 92, 1-12.
Oswald, J. (1951). Signaux aletoires a spectre limite. Cables et transmissiones, 5, 158-177.
Parzen, E. (1956). A simple proof and some extensions of the sampling theorem (Tech. Rep. No. 7).
Rozanov, Y. A. (1967). Stationary Random Processes. San Francisco, Calif.: Holden-Day Inc.
Shannon, C. E. (1948). A mathematical theory of communication. Bell System Technical Journal, 27, 623-656.
Shannon, C. E. (1949). Communication in the presence of noise. Proceedings of the I.R.E., 37, 10-21.
Whittaker, E. T. (1915). On the functions which are represented by the expansion of the interpolation theory. Proc. Roy. Soc. Edingburgh, Sect. A, 35, 181-194.
Yaglom, A. M. (1949). On problems about the linear interpolation of stationary random sequences and processes. Uspehi Matem. Nauk (N.S.), 4, 173-178.
Yaglom, A. M. (1987). Correlation theory of stationary and related random functions, Vol. I & II. New York: Springer-Verlag.
Downloads
Published
Issue
Section
License
The Austrian Journal of Statistics publish open access articles under the terms of the Creative Commons Attribution (CC BY) License.
The Creative Commons Attribution License (CC-BY) allows users to copy, distribute and transmit an article, adapt the article and make commercial use of the article. The CC BY license permits commercial and non-commercial re-use of an open access article, as long as the author is properly attributed.
Copyright on any research article published by the Austrian Journal of Statistics is retained by the author(s). Authors grant the Austrian Journal of Statistics a license to publish the article and identify itself as the original publisher. Authors also grant any third party the right to use the article freely as long as its original authors, citation details and publisher are identified.
Manuscripts should be unpublished and not be under consideration for publication elsewhere. By submitting an article, the author(s) certify that the article is their original work, that they have the right to submit the article for publication, and that they can grant the above license.
How to Cite
