On infinite past predictability of cyclostationary signals
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...
| Autores: | , |
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| Formato: | artículo |
| Fecha de publicación: | 2022 |
| País: | España |
| Recursos: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/366797 |
| Acesso em linha: | https://hdl.handle.net/2117/366797 https://dx.doi.org/10.1109/LSP.2022.3149705 |
| Access Level: | acceso abierto |
| Palavra-chave: | Cyclostationary waves Signal processing -- Digital techniques Toeplitz matrices Szegö’s theorem Cyclostationarity Cyclic Wiener filtering Periodically Toeplitz matrices Spectral coherence Tractament del senyal --Tècniques digitals Toeplitz, Operadors de Àrees temàtiques de la UPC::Enginyeria de la telecomunicació::Processament del senyal::Processament del senyal en les telecomunicacions |
| Resumo: | 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-Szeg 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. |
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