Estimation of renewal point process aftereffect character on the basis of multiscale correlation analysis methods

 

V. E. Antciperov

Kotel’nikov Institute of Radio-engineering and Electronics of RAS

 

The paper is received on June 4, 2015 

 

Abstract: This paper discusses the application of multiscale correlation analysis to the problem of evaluating the characteristics of wideband pulse processes with independent intervals (point processes with limited aftereffects – renewal processes). It is shown that for the averaged multiscale (cone kernel) representations it is possible, by using the technique of analytic spectra and, accordingly, the methods of the theory of functions of a complex variable, to simplify significantly their appearance. The latter greatly facilitates the dependence of representation characteristics on the process parameters such as average intensity, its variability, character of aftereffects, etc.  Basing on the analytical dependences found the paper suggests a construction of the corresponding estimates formed by sampled data – pulse processes realizations. Among the cases in which it is possible to carry out the analytical calculation to the final quadrature the case of a stationary flow and the case of sudden stationarity changes are considered.

Key words:  point processes, time−frequency analysis, wideband pulse processes, multiscale correlational analysis, analytic spectra.