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Cyclostationarity: Half a Century of Research

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ARTICLE IN PRESS Signal Processing 86 (2006) 639–697 www.elsevier.com/locate/sigpro Review Cyclostationarity: Half a century of research William A. Gardnera, Antonio Napolitanob,Ã, Luigi Paurac aStatistical Signal Processing Incorporated (SSPI), 1909 Jefferson Street, Napa, CA 94559, USA bUniversita` di Napoli ‘‘Parthenope’’, Dipartimento per le Tecnologie, via Acton 38, I-80133 Napoli, Italy cUniversita` di Napoli ‘‘Federico II’’, Dipartimento di Ingegneria Elettronica e delle Telecomunicazioni, via Claudio 21, I-80125 Napoli, Italy Received 22 December 2004; accepted 29 June 2005 Available online 6 September 2005 Abstract In this paper, a concise survey of the literature on cyclostationarity is presented and includes an extensive bibliography. The literature in all languages, in which a substantial amount of research has been published, is included. Seminal contributions are identified as such. Citations are classified into 22 categories and listed in chronological order. Both stochastic and nonstochastic approaches for signal analysis are treated. In the former, which is the classical one, signals are modelled as realizations of stochastic processes. In the latter, signals are modelled as single functions of time and statistical functions are defined through infinite-time averages instead of ensemble averages. Applications of cyclostationarity in communications, signal processing, and many other research areas are considered. r 2005 Elsevier B.V. All rights reserved. Keywords: Cyclostationarity; Almost-cyclostationary time series; Almost-cyclostationary processes; Bibliography Contents 1. Introduction . 641 2. General treatments. 642 3. General properties and structure of stochastic processes and time-series . 642 3.1. Introduction . 642 3.2. Stochastic processes . 643 3.2.1. Continuous-time processes . 643 3.2.2. Discrete-time processes . 645 ÃCorresponding author. Tel.: +39 081 768 37 81; fax: +39 081 768 31 49. E-mail addresses: [email protected] (W.A. Gardner), [email protected] (A. Napolitano), [email protected] (L. Paura). 0165-1684/$ - see front matter r 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.sigpro.2005.06.016 ARTICLE IN PRESS 640 W.A. Gardner et al. / Signal Processing 86 (2006) 639–697 3.3. Time series . 646 3.3.1. Continuous-time time series . 646 3.3.2. Discrete-time time series . 648 3.4. Link between the stochastic and fraction-of-time approaches . 649 3.5. Complex processes and time series . 649 3.6. Linear filtering . 650 3.6.1. Structure of linear almost-periodically time-variant systems . 650 3.6.2. Input/output relations in terms of cyclic statistics . 650 3.7. Product modulation . 651 3.8. Supports of cyclic spectra of band limited signals . 652 3.9. Sampling and aliasing. 653 3.10. Representations by stationary components . 654 3.10.1. Continuous-time processes and time series . 654 3.10.2. Discrete-time processes and time series. 655 4. Ergodic properties and measurement of characteristics . 656 4.1. Estimation of the cyclic autocorrelation function and the cyclic spectrum . 656 4.2. Two alternative approaches to the analysis of measurements on time series . 657 5. Manufactured signals: modelling and analysis . 658 5.1. General aspects . 658 5.2. Examples of communication signals. 659 5.2.1. Double side-band amplitude-modulated signal . 659 5.2.2. Pulse-amplitude-modulated signal . 659 5.2.3. Direct-sequence spread-spectrum signal . 660 6. Natural signals: modelling and analysis . 661 7. Communications systems: analysis and design . 661 7.1. General aspects . 661 7.2. Cyclic Wiener filtering . 661 8. Synchronization. 663 8.1. Spectral line generation. 663 9. Signal parameter and waveform estimation . 663 10. Channel identification and equalization . 664 10.1. General aspects . 664 10.2. LTI-system identification with noisy-measurements . 664 10.3. Blind LTI-system identification and equalization. 665 10.4. Nonlinear-system identification . 665 11. Signal detection and classification, and source separation . 665 12. Periodic AR and ARMA modelling and prediction. 666 13. Higher-order statistics . 666 13.1. Introduction . 666 13.2. Higher-order cyclic statistics . 667 13.2.1. Continuous-time time series . 667 13.2.2. Discrete-time time series . 669 14. Applications to circuits, systems, and control . 670 15. Applications to acoustics and mechanics . 670 16. Applications to econometrics . 671 17. Applications to biology . 671 18. Level crossings . 671 19. Queueing . 671 20. Cyclostationary random fields. 671 21. Generalizations of cyclostationarity . 671 21.1. General aspects . 671 ARTICLE IN PRESS W.A. Gardner et al. / Signal Processing 86 (2006) 639–697 641 21.2. Generalized almost-cyclostationary signals . 672 21.3. Spectrally correlated signals . 672 References . ..
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