On Infinite Past Predictability of Cyclostationary Signals

Abstract

This paper explores the asymptotic spectral decomposition of periodically Toeplitz matrices with finite summable elements. As an alternative to polyphase decomposition and other approaches based on Gladyshev representation, the proposed route exploits the Toeplitz structure of cyclic autocorrelation matrices, thus leveraging on known asymptotic results and providing a more direct link to the cyclic spectrum and spectral coherence. As a concrete application, the problem of cyclic linear prediction is revisited, concluding with a generalized Kolmogorov-Szegö theorem on the predictability of cyclostationary signals. These results are finally tested experimentally in a prediction setting for an asynchronous mixture of two cyclostationary pulse-amplitude modulation signals.