The reflection method with a change of sign in problems of the quality analysis of signal detection

D. V. Yevgrafov

doi:10.3103/S0735272710060075

Authors

D. V. Yevgrafov Igor Sikorsky Kyiv Polytechnic Institute, Ukraine https://orcid.org/0000-0001-9651-1558

DOI:

https://doi.org/10.3103/S0735272710060075

Keywords:

signal detection, Markov process

Abstract

The reflection method with a change of sign, initially used as a technique for solving the first boundary value problem of the heat conduction equation, has been extended for allowing us to elucidate the solution of earlier known problems of the quality analysis of signal detection algorithms using the tool of Markov processes and also to derive an expression for the probability of finding the absolute maximum of the normal stationary Markov process in the negative half-plane of values. A comparative analysis with a similar probability was performed for the root-mean-square differentiable process.

References

A. N. Tikhonov and A. A. Samarskii, Equations of the Mathematical Physics. Textbook for Universities (Nauka, Moscow, 1972) [in Russian].

A. P. Trifonov, “Reception of Signal Having the Unknown Duration against the Background of White Noise,” Radiotekh. Elektron. 22, No. 1, 90 (1977).

V. A. Bakut, Signal Detection Theory (Radio i Svyaz’, Moscow, 1984) [in Russian].

A. P. Trifonov and Yu. S. Shinakov, Joint Discrimination of Signals and Estimation of their Parameters against the Background of Interferences (Radio i Svyaz’, Moscow, 1986) [in Russian].

V. I. Tikhonov and M. A. Mironov, Markov Processes (Sov. Radio, Moscow, 1977) [in Russian].

V. I. Tikhonov and V. N. Kharisov, Statistical Analysis and Synthesis of Radio Devices and Systems: Textbook for Higher Educational Institutions (Radio i Svyaz’, Moscow, 1991) [in Russian].

A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marichev, Integrals and Series. Special Functions (Nauka, Moscow, 1983) [in Russian].

D. V. Yevgrafov, Distribution of the Absolute Maximum in the Signal Detection Theory (MOU, NAOU, Kiev, 2005) [in Ukrainian], Issue 65, pp. 86–89.

A. P. Trifonov and V. K. Buteiko, “Reception of Signal with Unknown Amplitude and Length against the Background of White Noise,” Izv. Vyssh. Uchebn. Zaved., Radioelektron. 27(8), 28 (1984); Radioelectron. Commun. Syst. 27(8), 23 (1984).