In [J5], input/output relations in terms of cyclic higher-order statistics for multi-input multi-output linear almost-periodically time-variant systems that are excited by cyclostationary inputs are derived in both time and frequency domains. Both continuous- and discrete-time systems are considered. For a single-input single-output linear time-invariant system, the Wiener system identification formula based on second-order cyclic spectra is generalized to higher-order statistics. The problem of reconstructing cyclic higher-order statistics of a continuous-time-series from its samples is addressed and a sufficient condition on the sampling rate to prevent aliasing is stated. Examples of application of the theory are presented.
In [J6], the higher-order wide-sense stationarity or cyclostationarity properties of a continuous-time-series and those of the discrete-time-series of its samples are related. It is shown that the higher-order wide-sense stationarity or cyclostationarity of a strictly band limited continuous-time-series can be analyzed by examining that exhibited by the discrete-time-series of its samples provided that the sampling rate is sufficiently high.
In [J7], the role played by the higher-order wide-sense cyclostationarity properties in Rice’s representation of a signal is investigated. Specifically, formulas relating higher-order cyclic spectra of the analytic signal, the complex envelope, and the in-phase and quadrature components of a signal exhibiting cyclostationarity are derived. With reference to strictly band-limited signals, inclusion relationships for the spectral supports (in the space of the cycle and spectral frequencies) of the considered higher-order spectra are determined.
In [J8], the effects of multirate systems on the higher-order wide-sense cyclostationarity properties of discrete time-series are investigated. Starting from the consideration of the basic multirate building blocks, viz., M-fold decimators and L-fold interpolators, results for typical interconnections are derived. The problem of eliminating the images in the cyclic higher-order spectra of an interpolated time-series is addressed. Moreover, the problem of avoiding aliasing (in both cycle and spectral frequency domains) in the cyclic higher-order spectra of a decimated time-series is considered. Finally, a sufficient condition to avoid both aliasing and imaging effects in the cyclic higher-order spectra of a time-series decimated by a fractional factor is derived.
In [J10], a new nonparametric algorithm for the identification of linear time-invariant systems is proposed. The method is based on the cyclic correlations of the input and output signals with a nonlinear transformation of the input signal. Consequently, although it exploits the higher-order cyclostationarity properties of the input and output signals, its computational complexity and its performance are comparable to those of methods based on second-order statistics.
In [J11], median-based estimation methods for the cyclic polyspectrum are proposed. The algorithms do not require a priori knowledge of the .-submanifolds, that is, they do not require the knowledge of all of the lower-order cycle frequencies of the time-series available for the estimation of the cyclic polyspectrum. Therefore, such methods are particularly useful when the cyclostationarity of the signals under consideration is not completely known.
In [J21], a concise survey of the literature on cyclostationarity up to year 2005 is presented and includes an extensive bibliography (786 references). The literature in all languages, in which a substantial amount of research has been published, is included. Seminal contributions are identified a such. Citations are classified into twenty two categories and listed in chronological order. Both stochastic and nonstochastic approaches for signal analysis are treated. Applications of cyclostationarity in communications, signal processing, and many other research areas are considered.
A concise survey of the literature on cyclostationarity from year 2006 to 2015 is presented in [J36] and an extensive bibliography included. The problems of statistical function estimation, signal detection, and cycle frequency estimation are reviewed. Applications in communications are addressed. In particular, spectrum sensing and signal classification for cognitive radio, source location, MMSE filtering, and compressive sensing are discussed. Limits to the applicability of the cyclostationary signal processing and generalizations of cyclostationarity to overcome these limits are addressed in the companion paper "Cyclostationarity: Limits and generalizations" [J37].
In [J38], for almost-cyclostationary processes, sufficient conditions are derived, such that estimates of the second-order cyclic probabilistic functions with estimated cycle frequencies are mean-square consistent and asymptotically complex normal. Cyclic (conjugate) autocorrelation functions and (conjugate) cyclic spectra are considered. Under the derived conditions, asymptotically, as the data-record length approaches infinity, the estimates of cyclic statistics with estimated cycle frequencies have the same complex normal distribution as the case of exactly known cycle frequencies. The results are applied to the detection of a moving cyclostationary source in the presence of strong Doppler effect and for low values of SNR.
In [J40], the problem of bandpass sampling a continuous-time almost-cyclostationary signal is addressed. Sufficient conditions are derived such that the cyclic spectra of the complex envelope of the continuous-time signal can be reconstructed by samples obtained by bandpass sampling the continuous-time bandpass real signal.