Distribution of intervals between spikes of random process: erroneous arguments and reality

Authors

DOI:

https://doi.org/10.3103/S0735272711110082

Keywords:

Rice distribution, stationery process spikes, initial time point

Abstract

It is proven a fallibility of known dependence of distribution of intervals of spikes of stationery process on distribution of its absolute maximum. It is shown that it resulted in delusion about simple type of these distributions and possibility of generalization of results on non-stationery process.

References

S. O. Rice, “Mathematical Analysis of Random Noise,” Bell Sys. Tech. J. 23, No. 3 (1944), 24, No. 1, (1945).

V. I. Tikhonov, Random Processes Spikes (Nauka, Moscow, 1970) [in Russian].

V. F. Shukaylo, “About Distribution of Absolute Maximums of Random Processes,” Radiotekh. Elektron. 13, No. 6, 996 (1968).

D. V. Yevgrafov, “Distribution of Time Intervals Determining the First Instant when a Stationary Process Reaches the Set Level,” Izv. Vyssh. Uchebn. Zaved., Radioelektron. 52(10), 14 (2009) [Radioelectron. Commun. Syst. 52(10), 522 (2009)].

D. V. Yevgrafov, “Distribution of Absolute Maximum in a Theory of Signals Detection,” in Proc. of Academy MOU, NAOU (Kyiv, 2005), Vol. 65, pp. 86–89.

D. V. Yevgrafov, “The Integro-Differential Equation for Distribution of the Absolute Maximum of a Gaussian Stationary Process,” Izv. Vyssh. Uchebn. Zaved., Radioelektron. 46(5), 25 (2003); Radioelectron. Commun. Syst. 46(5), 20 (2003).

D. V. Yevgrafov, Distribution of Absolute Maximum in a Theory of Signals Detection with Radio Control Facilities (VIKNU, Kyiv, 2005), Vol. 1, pp. 46–51.

D. V. Yevgrafov, “Strict Analysis of Algorithms for Detection of Signals of Unknown Duration,” Izv. Vyssh. Uchebn. Zaved., Radioelektron. 49(10), 76 (2006); Radioelectron. Commun. Syst. 49(10), 62 (2006).

D. V. Yevgrafov, “Algorithm characteristics for detection of signals of unknown energy,” Izv. Vyssh. Uchebn. Zaved., Radioelektron. 50(12), 65 (2007) [Radioelectron. Commun. Syst. 50(12), 697 (2007)].

Ya. A. Fomin, The Theory of Spikes of Random Processes (Svyaz’, Moscow, 1980) [in Russian].

D. V. Yefgrafov, “Influence of Spectral Characteristics of a Process on Its Absolute Maximum Distribution,” Izv. Vyssh. Uchebn. Zaved., Radioelektron. 52(8), 48 (2009) [Radioelectron. Commun. Syst. 52(8), 431 (2009)].

Ya. A. Fomin, “Average Time of the First Reach of Definite Area Limit by Ergodic Random Process,” Radiotekh. Elektron. 12, No. 6, 1090 (1967).

Published

2011-11-01

Issue

Section

Research Articles