Multirate processing of time series exhibiting higher order cyclostationarity

The paper is aimed at investigating the effects of multirate systems on the higher order wide-sense cyclostation-arity (WSCS) properties of discrete-time series. To this end, definitions and properties of the cyclic higher order statistics, which were recently introduced for continuous-time series in the fraction-of-time probability framework, are first extended to discrete-time series. Then, 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.