Cyclic spectral analysis from the averaged cyclic periodogram
World Congress, Volume # 16 | Part# 1
Roger Boustany; Jerome Antoni
Digital Object Identifier (DOI)
signal processing,spectral analysis,averaged periodogram,cyclostationary signals,cyclic spectral estimation,cyclic leakage
The theory of cyclostationarity has emerged as a new approach to characterizing a certain type of nonstationary signals. Many aspects of the spectral analysis of cyclostationary signals have been investigated but were essentially based on the use of the smoothed cyclic periodogram. This paper proposes a cyclic spectral estimator based on the averaged cyclic periodogram which benefits from better implementation properties. It shows that an unexpected but important condition for this estimator to be valid is to set enough overlap between adjacent segments in order to prevent cyclic leakage. It proves that setting the percentage of overlap to 75% with a hanning window, or 50% with a half-sine window fixes the problem. It also shows that in certain situations the cyclic leakage associated with the averaged cyclic periodogram can be made exactly zero, in contrast with the smoothed cyclic periodogram. Illustrative examples finally confirm the obtained results, where it is also demonstrated how to use them for efficiently estimating the Wigner-Ville spectrum.
 Antoni, J., F. Bonnardot, A. Raad and M. El Badaoui (2004). Cyclostationary modelling of rotating machine vibration signals. Mechanical Systems and Signal Processing 18(6), 1285-1314.  Dandawate, A. and G. Giannakis (1994). Nonparametric polyspectral estimators for kth-order (almost) cyclostationary processes. IEEE Trans. on Information theory 40(1), 67-54.  Gardner, W. (1986). Measurement of spectral correlation. IEEE trans. on Acoustics, Speech, and Signal Processing 34(5), 1111-1123.  Gardner, W. (1990). Introduction to Random Processes . 2nd ed.. McGraw-Hill. Chap.12.  Gardner, W. (1991). Exploitation of spectral redundancy in cyclostationary signals. IEEE Signal Processing Magazine pp. 14-36.  Giannakis, G. (1998). Cyclostationary signal analysis. in The Digital Signal Processing Handbook , IEEE Press. Chap. 5.  Hurd, H. (1989). Nonparametric time series analysis for periodically correlated processes. IEEE trans. on Information theory 35(2), 350-359.  Roberts, R., W. Brown and H. Loomis (1991). Computationally efficient algorithms for cyclic spectral analysis. IEEE Signal Processing Magazine pp. 38-49.