Variability method for cyclo-period estimation of cyclostationary signals
World Congress, Volume # 16 | Part# 1
Authors
Jiandong Wang; Tongwen Chen; Biao Huang
Digital Object Identifier (DOI)
10.3182/20050703-6-CZ-1902.00029
Page Numbers:
28-28
Index Terms
cyclostationary signals,cyclo-period estimation,blocking,variability
Abstract
This paper presents a new method, named as the variability method, to estimate the cyclo-period of a discrete-time cyclostationary signal. The method is essentially based on the time-varying correlation and/or mean, whose estimators are associated with some statistics of blocked signals; a plot of variability of these statistics as a function of the blocking operator index visually reveals a periodic pattern, from which the cyclo-period is obtained. The variability method is validated via simulation and real-life examples.
References
[1] Box, G. E. P., G. M. Jenkins and G. C. Reinsel
(1994). Time Series Analysis: Forecasting and
Control, Englewood Cliffs, NJ: Prentice-Hill.
[2] Dandawaté, A. V. and G. B. Giannakis (1994).
Statistical tests for presence of cyclostationarity,
IEEE Trans. Signal Processing, 42(9),
pp. 2355-2369.
[3] Gardner, W. A. (1990). Identification of systems
with cyclostationary input and correlated input/output
measurement noise, IEEE Trans.
Automat. Control, 35(4), pp. 449-452.
[4] Gardner, W. A. (1994). An introduction to cyclostationary
signals, in Cyclostationarity in
Communications and Signal Processing, W.
A. Gardner, Ed., Piscataway, NJ: IEEE Press.
[5] Giannakis, G. B. (1995). Polyspectral and cyclostationary
approaches for identification of
closed-loop systems, IEEE Trans. Automat.
Control, 40(5), pp. 882-885.
[6] Giannakis, G. B. (1999). Cyclostationary signal
analysis, in Digital Signal Processing Handbook
, Boca Raton: CRC Press LLC.
[7] Gladyshev, E. G. (1961). Periodically correlated
random sequence, Soviet Math., 2, pp. 385-
388.
[8] Herbst, L. J. (1965). The statistical Fourier analysis
of variances, J. R. Statist. Soc., B 27,
pp. 159-165.
[9] Hurd, H. L. and N. L. Gerr (1991). Graphical
methods for determining the presence of periodic
correlation, J. Times Ser. Anal., 12(4),
pp. 337-350.
[10] Martin, D. E. K. and B. Kedem (1993). Estimation
of the period of periodically correlated sequences,
J. Times Ser. Anal., 14(2), pp. 193-
205.
[11] Martin, D. E. K. (1999). Detection of periodic
autocorrelation in time series data via zero-crossing,
J. Times Ser. Anal., 20(4), pp. 435-
452.
[12] Meyer, R. A. and C. S. Burrus (1975). A unified
analysis of multirate and periodically time-varying
digital filters, IEEE Trans. Circuits
Syst., 22(3), pp. 162-168.
[13] Ohno, S. and H. Sakai (1996). Optimization of filter
banks using cyclostationary spectral analysis,
IEEE Trans. Signal Processing, 44(11),
pp. 2718-2725.
[14] Papoulis, A. (1965), Probability, Random Variables
and Stochastic Processes, New York:
McGraw-Hill.
[15] Sakai, H. and S. Ohno (1997). Theory of cyclostationary
processes and its application,
in Statistical Methods in Control and Signal
Processing, pp. 327-354, New York: Marcel
Dekker.
[16] Sathe, V. P. and P. P. Vaidyanathan (1993).
Effects of multirate systems on the statistical
properties of random signals, IEEE Trans.
Signal Processing, 41(1), pp. 131-146.
[17] Sun, L., H. Ohmori and A. Sano (2000). Frequency
domain approach to closed-loop identification
based on output inter-sampling scheme,
Proc. of the American Control Conference, 3,
pp. 1802-1806.
[18] Tian, C. J. (1988). A limiting property of sample
autocovariances of periodically correlated
processes with application to period determination,
J. Times Ser. Anal., 9(4), pp. 411-
417.
[19] Tong, L., G. Xu, and T. Kailath (1994).
Blind identification and equalization based
on second-order statistics: a time domain approach,
IEEE Trans. Inform. Theory, 40(2),
pp. 340-349.
[20] Tong, L., G. Xu, B. Hassibi and T. Kailath
(1995). Blind identification and equalization
based on second-order statistics: a frequency-domain
approach, IEEE Trans. Inform. Theory
, 41(1), pp. 329-334.
[21] Wang, J., T. Chen and B. Huang (2004). Closed-loop
identification via output fast sampling,
J. Process Control, 14(5), pp. 555-570.
[22] Vaidyanathan, P. P. (1993). Multirate Systems
and Filter Banks, Englewood Cliffs, NJ:
Prentice-Hall.
