| Many real life signals occurring in diverse environments such as communications, astronomy, meteorology, biological and mechanically vibrating systems exhibit an almost periodically time-varying, nonstationary behavior, and are termed as almost cyclostationary processes. For mathematical convenience it is common to impose a stationary model on almost cyclostationary processes, and thus, inefficiently utilize the available information. Existing approaches which avoid stationarizing real, discrete-time almost cyclostationary signals are based only on the second-order statistics of the processes and do not prove consistency of the statistical estimators. In this thesis, we establish that cyclic-cumulants and polyspectra are valuable tools for jointly exploiting cyclostationarity and higher-order statistics (HOS) in signal processing. Contrary to second-order cyclic-statistics cyclic-HOS are capable of identifying mixed-phase linear systems and are insensitive to (even cyclostationary) Gaussian noise among other types of disturbances. We develop consistent and asymptotically normal estimators for the kth-order cyclic-cumulants and polyspectra of almost cyclostationary processes. Asymptotic covariance expressions are derived along with their computational forms. Using the normality of sample cyclic-statistics, asymptotically chi-squared tests are developed for detecting and estimating cycles present in the kth-order cyclic-cumulants and polyspectra. To demonstrate the usefulness of the proposed estimators the problem of estimating the cumulants and polyspectra, along with the asymptotic distributions, of AM signals and processes with missing observations is addressed. Next, kth-order cyclic-statistics based input/output and output only algorithms are developed for identification of linear (almost) periodically time-varying systems. Asymptotically optimal schemes in the cyclic-statistics domain are derived for detecting and classifying cyclostationary signals in noise of unknown distribution. Finally, some generalizations of the consistency results are presented, connections with the time-frequency representations of cyclostationary signals are made, and the importance of considering structured nonstationarity is emphasized. Advantages over existing algorithms are stated and simulations are performed to illustrate some of the schemes. |
