Processes encountered in statistical signal processing, communications, and time series analysis applications are often assumed stationary. | Giannakis . Cyclostationary Signal Analysis Digital Signal Processing Handbook Ed. Vijay K. Madisetti and Douglas B. Williams Boca Raton CRC Press LLC 1999 1999 by CRC Press LLC 17 Cyclostationary Signal Analysis Georgios B. Giannakis University of Virginia Introduction Definitions Properties Representations Estimation Time-Frequency Links Testing Estimating Cyclic Statistics Links with Time-Frequency Representations Testing for Cyclostationarity CS Signals and CS-Inducing Operations Amplitude Modulation Time Index Modulation Fractional Sampling and Multivariate Multirate Processing Periodically Varying Systems Application Areas CS Signal Extraction Identification and Modeling Concluding Remarks Acknowledgments References Introduction Processes encountered in statistical signal processing communications and time series analysis applications are often assumed stationary. The plethora of available algorithms testifies to the need for processing and spectral analysis of stationary signals see . 42 . Due to the varying nature of physical phenomena and certain man-made operations however time-invariance and the related notion of stationarity are often violated in practice. Hence study of time-varying systems and nonstationary processes is well motivated. Research in nonstationary signals and time-varying systems has led both to the development of adaptive algorithms and to several elegant tools including short-time or running Fourier transforms time-frequency representations such as the Wigner-Ville a member of Cohen s class of distributions Loeve s and Karhunen s expansions leading to the notion of evolutionary spectra and time-scale representations based on wavelet expansions see 37 45 and references therein . Adaptive algorithms derived from stationary models assume slow variations in the underlying system. On the other hand time-frequency and time-scale representations promise applicability to general nonstationarities and .
