Spectral factorization of linear periodic systems with application to the optimal prediction of periodic ARMA models

✍ Scribed by Sergio Bittanti; Giuseppe De Nicolao

• Publisher: Elsevier Science
• Year: 1993
• Tongue: English
• Weight: 580 KB
• Volume: 29
• Category: Article
• ISSN: 0005-1098
• DOI: 10.1016/0005-1098(93)90149-n

✦ Synopsis

A cyciostationary process is a stochastic process whose statistical parameters, such as mean and autocorrelation, exhibit suitable periodicity. In this paper, we consider the cyclospectrai factorization problem which consists of finding a Markovian (state-space) realization of a given cyclostationary process. It is shown that a significant class of periodic state-space representations is in a one-to-one correspondence with the periodic solutions of a difference periodic Riccati equation. This result is applied to the solution of the prediction problem for ARMA models with periodically varying coefficients. If the periodic ARMA model is minimum-phase, the optimal predictor is given a simple input-output expression that generalizes the wellknown one for time-invariant ARMAs. Otherwise, the computation of the optimal predictor calls for the solution of a cyclospectral factorization problem.