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The resultant of a large number of events of random phase

Published online by Cambridge University Press:  24 October 2008

C. Domb
C. Domb
Affiliation:
Department of Scientific ResearchAdmiralty
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Extract

Rayleigh's method of deducing the probability distribution of the amplitude of the sum of n equal vibrations of random phase is generalized to the case when the amplitude of each vibration is a definite function of its phase. The same method is applied to the shot effect and it enables the distribution of random noise to be obtained. Campbell's Theorem and its generalizations can then be deduced from this.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 42 , Issue 3 , October 1946 , pp. 245 - 249
Copyright
Copyright © Cambridge Philosophical Society 1946

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References

REFERENCES

(1)Chandrasekhar, S.Rev. Mod. Phys. 15 (1943), 1.CrossRefGoogle Scholar
(2)Rayleigh, . Theory of Sound, vol. 1, § 42a.Google Scholar
(3)Rice, S. O.Bell Syst. Tech. J. 23 (1944), 282.CrossRefGoogle Scholar