Open Access Open Access  Restricted Access Subscription Access
Linear transformation of PCRP-signal

Coherence function of interrelated periodically nonstationary random processes

Ihor N. Yavorskyj, Roman Yuzefovych, Ivan Y. Matsko, Zbigniew Zakrzewski


A coherence function characterizing the correlation between harmonic components of two signals that are described by periodically correlated random processes has been proposed. Such function is shown to be invariant with regard to linear transformations of signals. A formula for coherence function is concretized for the amplitude- and phase-modulated signals.


periodically nonstationary random process; harmonic correlation; coherence function; linear transformations

Full Text:



MIRSKII, G.Y. Stochastic Interaction Characteristics and their Measurements. Moscow: Energoizdat, 1982 [in Russian].

BENDAT, J.S.; PIERSOL, A.G. Random Data: Analysis and Measurement Procedures, 4th ed. Wiley, 2010.

BENDAT, J.S.; PIERSOL, A.G. Engineering Applications of Correlation and Spectral Analysis, 2nd ed. Wiley, 1993.

GARDNER, W.A. (ed.), Cyclostationarity in Communications and Signal Processing. New York: IEEE Press, 1994.

NAPOLITANO, A. Generalizations of Cyclostationary Signal Processing: Spectral Analysis and Applications. Wiley-IEEE Press, 2012.

GARDNER, WILLIAM A.; NAPOLITANO, ANTONIO; PAURA, LUIGI. Cyclostationarity: Half a century of research. Signal Processing, 2006, v.86, n.4, p.639-697, DOI:

YAVORSKYJ, I.M. Mathematical Models and Analysis of Stochastic Oscillations. Lviv: FMI NANU, 2013 [in Ukrainian].

HINICH, M.J. A statistical theory of signal coherence. IEEE J. Oceanic Engineering, Apr. 2000, v.25, n.2, p.256-261, DOI:

GARDNER, W.A. Introduction to Random Processes with Application to Signals and Systems. New York: Macmillan, 1985.

GARDNER, W.A. On the spectral coherence of nonstationary processes. IEEE Trans. Signal Process, Feb. 1991, v.39, n.2, p.424-430, DOI:

GARDNER, W.A. Exploitation of spectral redundancy in cyclostationary signals. IEEE SP Magazine (Signal Processing), Apr. 1991, v.8, n.2, p.14-36, DOI:

HURD, H.L.; MIAMEE, A. Periodically Correlated Random Sequences. Spectral Theory and Practice. New Jersey: Wiley–Interscience, 2007, 353 p.

© Radioelectronics and Communications Systems, 2004–2020
When you copy an active link to the material is required
ISSN 1934-8061 (Online), ISSN 0735-2727 (Print)
tel./fax +38044 204-82-31, 204-90-41