Discrete LS estimates of correlation function of bi-periodically correlated random signals

Ihor N. Yavorskyj; Oksana Yu. Dzeryn; Roman Yuzefovych

doi:10.3103/S0735272720030036

Authors

Ihor N. Yavorskyj Karpenko Physico-Mechanical Institute of NASU; University of Technology and Life Sciences, Ukraine https://orcid.org/0000-0003-0243-6652
Oksana Yu. Dzeryn Karpenko Physico-Mechanical Institute of NASU, Ukraine https://orcid.org/0000-0002-8768-0218
Roman Yuzefovych Karpenko Physico-Mechanical Institute of NASU; Lviv Polytechnic National University, Ukraine https://orcid.org/0000-0001-5546-453X

DOI:

https://doi.org/10.3103/S0735272720030036

Keywords:

bi-periodically correlated random process, correlation function estimation, least squares method, asymptotical unbiasedness, asymptotical consistency, leakage effect, discretization step

Abstract

Analysis of discrete estimates of bi-periodically correlated random processes (BPCRP)—mathematical models of signals with double stochastic periodicity was performed using least squares (LS) technique. It is shown that LS utilization allows to avoid systematic errors related to leakage effect. Expressions for estimate bias and dispersion were obtained, allowing determination systematic and mean square errors depending on discretization step, sample number and signal parameters were obtained. For quadrature BPCRP model discrete and continuous dispersions of LS estimation of correlation components were compared. Recommendations for discretization step are given.

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