Mathematical Analysis of Random Noise

1945/01/01 by S. O. Rice · 14 citations
Computer Science · Physics and Astronomy · #Neural Networks and Applications #Scientific Research and Discoveries #Statistical Mechanics and Entropy

paper · doi:10.1002/j.1538-7305.1945.tb00453.x

crossref issued 1945/01/01 · crossref published 1945/01/01 · crossref published-print 1945/01/01 · openalex publication_date 1945/01/01 · crossref published-online 2013/07/29 · crossref created 2013/07/29 · crossref deposited 2020/10/14 · openalex created_date 2025/10/10 · crossref indexed 2026/07/31 · openalex updated_date 2026/08/01

Abstract

In this section we use the representations of the noise currents given in section 2.8 to derive some statistical properties of I(t). The first six sections are concerned with the probability distribution of I(t) and of its zeros and maxima. Sections 3.7 and 3.8 are concerned with the statistical properties of the envelope of I(t). Fluctuations of integrals involving I2(t) are discussed in section 3.9. The probability distribution of a sine wave plus a noise current is given in 3.10 and in 3.11 an alternative method of deriving the results of Part III is mentioned. Prof. Uhlenbeck has pointed out that much of the material in this Part is closely connected with the theory of Markoff processes. Also S. Chandrasekhar has written a review of a class of physical problems which is related, in a general way, to the present subject.22

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