On the Algorithmic Solvability of the Spectral Factorization and the Calculation of the Wiener Filter on Turing Machines

Holger Boche; Volker Pohl

doi:10.1109/ISIT.2019.8849557

On the Algorithmic Solvability of the Spectral Factorization and the Calculation of the Wiener Filter on Turing Machines

Holger Boche
, Volker Pohl

Chair of Theoretical Information Technology

Munich Center for Quantum Science and Technology (MCQST)
Technical University of Munich

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

10 Scopus citations

Abstract

The spectral factorization is an important operation in many different applications. This paper studies whether the spectral factor of a given computable spectral density can always be computed on an abstract machine (a Turing machine). It is shown that there are computable spectral densities with very comfortable analytic properties (smoothness and finite energy) such that the corresponding spectral factor can not be determined on a Turing machine. As an application, the paper discusses the possibility of calculating the optimal Wiener filter from computable spectral densities.

Original language	English
Title of host publication	2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	2459-2463
Number of pages	5
ISBN (Electronic)	9781538692912
DOIs	https://doi.org/10.1109/ISIT.2019.8849557
State	Published - Jul 2019
Event	2019 IEEE International Symposium on Information Theory, ISIT 2019 - Paris, France Duration: 7 Jul 2019 → 12 Jul 2019

Publication series

Name	IEEE International Symposium on Information Theory - Proceedings
Volume	2019-July
ISSN (Print)	2157-8095

Conference

Conference	2019 IEEE International Symposium on Information Theory, ISIT 2019
Country/Territory	France
City	Paris
Period	7/07/19 → 12/07/19

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10.1109/ISIT.2019.8849557

Cite this

Boche, H., & Pohl, V. (2019). On the Algorithmic Solvability of the Spectral Factorization and the Calculation of the Wiener Filter on Turing Machines. In 2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings (pp. 2459-2463). Article 8849557 (IEEE International Symposium on Information Theory - Proceedings; Vol. 2019-July). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ISIT.2019.8849557

Boche, Holger ; Pohl, Volker. / On the Algorithmic Solvability of the Spectral Factorization and the Calculation of the Wiener Filter on Turing Machines. 2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings. Institute of Electrical and Electronics Engineers Inc., 2019. pp. 2459-2463 (IEEE International Symposium on Information Theory - Proceedings).

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abstract = "The spectral factorization is an important operation in many different applications. This paper studies whether the spectral factor of a given computable spectral density can always be computed on an abstract machine (a Turing machine). It is shown that there are computable spectral densities with very comfortable analytic properties (smoothness and finite energy) such that the corresponding spectral factor can not be determined on a Turing machine. As an application, the paper discusses the possibility of calculating the optimal Wiener filter from computable spectral densities.",

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doi = "10.1109/ISIT.2019.8849557",

language = "English",

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Boche, H & Pohl, V 2019, On the Algorithmic Solvability of the Spectral Factorization and the Calculation of the Wiener Filter on Turing Machines. in 2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings., 8849557, IEEE International Symposium on Information Theory - Proceedings, vol. 2019-July, Institute of Electrical and Electronics Engineers Inc., pp. 2459-2463, 2019 IEEE International Symposium on Information Theory, ISIT 2019, Paris, France, 7/07/19. https://doi.org/10.1109/ISIT.2019.8849557

On the Algorithmic Solvability of the Spectral Factorization and the Calculation of the Wiener Filter on Turing Machines. / Boche, Holger; Pohl, Volker.
2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings. Institute of Electrical and Electronics Engineers Inc., 2019. p. 2459-2463 8849557 (IEEE International Symposium on Information Theory - Proceedings; Vol. 2019-July).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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N2 - The spectral factorization is an important operation in many different applications. This paper studies whether the spectral factor of a given computable spectral density can always be computed on an abstract machine (a Turing machine). It is shown that there are computable spectral densities with very comfortable analytic properties (smoothness and finite energy) such that the corresponding spectral factor can not be determined on a Turing machine. As an application, the paper discusses the possibility of calculating the optimal Wiener filter from computable spectral densities.

AB - The spectral factorization is an important operation in many different applications. This paper studies whether the spectral factor of a given computable spectral density can always be computed on an abstract machine (a Turing machine). It is shown that there are computable spectral densities with very comfortable analytic properties (smoothness and finite energy) such that the corresponding spectral factor can not be determined on a Turing machine. As an application, the paper discusses the possibility of calculating the optimal Wiener filter from computable spectral densities.

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Boche H, Pohl V. On the Algorithmic Solvability of the Spectral Factorization and the Calculation of the Wiener Filter on Turing Machines. In 2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings. Institute of Electrical and Electronics Engineers Inc. 2019. p. 2459-2463. 8849557. (IEEE International Symposium on Information Theory - Proceedings). doi: 10.1109/ISIT.2019.8849557

On the Algorithmic Solvability of the Spectral Factorization and the Calculation of the Wiener Filter on Turing Machines

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