Phase derivative distribution of signal and Gaussian noise sum

Authors

  • V. I. An Moscow State Technical University n.a. N. E. Bauman, Russian Federation

DOI:

https://doi.org/10.3103/S0735272709100082

Abstract

Characteristic function and integral function of the phase derivative distribution of harmonic signal and narrowband Gaussian noise sum are obtained for the case when the signal’s central frequency coincides with the central frequency of noise spectrum. It is shown that the power series for the distribution density of the phase derivative is determined by odd moments of the envelope.

References

B. R. Levin, Theoretical Basics of Statistical Radio-Engineering, Book 1 (Sov. Radio, Moscow, 1974) [in Russian].

V. I. An, “Distribution density of logarithmic derivative of signal and narrowband noise sum,” Radiotekhnika 61, No. 6, 18 (2006).

А. P. Prudnikov, Yu. А. Brychkov, and О. I. Marichev, Integrals and Series. Elementary Functions (Nauka, Moscow, 1981) [in Russian].

G. Bateman and А. М. Erdeyi, Higher Transcendental Functons, Vol. 2 (McGraw-Hill, New York, 1953; Nauka, Moscow, 1966).

М. Abramowitz and I. Stegun (ed.), Handbook on Mathematical Functions with Formulas, Graphs, and Mathematical Tables (Dover Publications, New York, 1972; Nauka, Moscow, 1979).

V. D. Alexandrov, “Distribution of simultaneous frequencies difference of two Gaussian processes,” Izv. Vyssh. Uchebn. Zaved., Radioelektron. 33(1), 87 (1990); Radioelectron. Commun. Syst. 33(1), 85 (1990).

G. Bateman and А. M. Erdeyi, Tables of Integral Transforms, Vol. 1 (McGraw-Hill, New York, 1954; Nauka, Moscow, 1969).

Published

2009-10-08

Issue

Section

Research Articles