Probabilistic characteristics of the envelope derivative for the sum of signal and narrow-band noise

V. I. An

doi:10.3103/S0735272710030039

Authors

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

DOI:

https://doi.org/10.3103/S0735272710030039

Keywords:

probability density, Gaussian noise

Abstract

Probability density and the formula for moments of the envelope derivative of the sum of harmonic signal and Gaussian narrow-band noise have been obtained. A new random function equal to the product of the envelope and phase derivative was introduced and the same probabilistic characteristics were determined for this function. Geometrical interpretation of the sum of signal and noise implies that the introduced function represents angular speed of rotation of the resultant vector.

References

V. I. Tikhonov, Nonlinear Transformations of Random Processes (Radio i Svyaz’, Moscow, 1986) [in Russian].

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

D. V. Evgrafov, “Dispersion of the derivative of the sum of harmonic signal and stationary Gaussian process under condition of detuning of the linear section of the receiver,” Izv. Vyssh. Uchebn. Zaved., Radioelektron. 40(1), 65 (1997); Radioelectron. Commun. Syst. 40(1), 52 (1997).

H. Bateman and A. Erdelyi, Higher Transcendental Functions, Vol. 2 (McGraw-Hill, New York, 1953; Nauka, Moscow, 1966).

B. N. Groznetskii and A. L. Shteinberg, “Probabilistic characteristics of the product of envelope and phase derivative of the narrow-band random process,” Izv. Vyssh. Uchebn. Zaved., Radioelektron. 42(7), 79 (1999); Radioelectron. Commun. Syst. 42(7), 75 (1999).

V. D. Zakharchenko, “Integral bandlimitedness criterion of radio signals,” Izv. Vyssh. Uchebn. Zaved., Radiofizika 18, No. 10, 923 (2000).

V. S. Sobolev and G. A. Kashcheeva, “Dispersion and spectral density of the product of instantaneous frequency and amplitude of multifrequency Doppler signal,” Radiotekh. Elektron. 30, No. 9, 1845 (1985).

V. I. An, “The mean value of derivative of phase modulus of the harmonic signal and Gaussian noise sum,” Izv. Vyssh. Uchebn. Zaved., Radioelektron. 51(11), 49 (2008) [Radioelectron. Commun. Syst. 51(11), 608 (2008)].