Asymptotic Analysis of Synchronous Signal Processing

Autor:	Vilà-Insa, Marc, Riba, Jaume
Rok vydání:	2024
Předmět:	Electrical Engineering and Systems Science - Signal Processing
Druh dokumentu:	Working Paper
Popis:	This paper extends various theoretical results from stationary data processing to cyclostationary (CS) processes under a unified framework. We first derive their asymptotic eigenbasis, which provides a link between their Fourier and Karhunen-Lo\`eve (KL) expansions, through a unitary transformation dictated by the cyclic spectrum. By exploiting this connection and the optimalities offered by the KL representation, we study the asymptotic performance of smoothing, filtering and prediction of CS processes, without the need for deriving explicit implementations. We obtain minimum mean squared error expressions that depend on the cyclic spectrum and include classical limits based on the power spectral density as particular cases. We conclude this work by applying the results to a practical scenario, in order to quantify the achievable gains of synchronous signal processing. Comment: 14 pages, 7 figures, submitted to the IEEE for possible publication
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2403.18445 Zobrazit plný text záznamu View this record from Arxiv