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.