Statistical Analysis of the 2^mth-Order Chirp Cyclostationary Processes

— Cyclostationary signals are usually encountered in practical applications, which are properly characterized by cyclic statistics. The chirp cyclostationary (CCS) model, which has recently been proposed as a generalization of the cyclostationary model, is demonstrated to be a more appropriate model for communications and radar systems. However, the cyclic statistics of CCS signals are limited in practical applications because they are zero-value or band-unlimited. The main reason for this is that they are not compatible with the bases of a Fourier transform. In this study, affine cyclic statistics of CCS processes are defined as associated with the affine Fourier transform (AFT). Specifically, the cross time and lags in the 2^mnd-order moment/cumulant without conjugate term are proven to be separable, based on which a framework for affine cyclic statistics is proposed. As special cases, three types of affine cyclic statistics are discussed in detail. Especially, the affine cyclic moment spectrum is proven to be the moment of the AFT spectrum of CCS processes, which is useful in designing estimators; application of the affine cyclic cumulant in the direction of arrival estimation of CCS sources is introduced; applications of the affine cyclic moment in parameter estimation and electrocardiogram feature extraction are simulated.