Robustness of the inner-outer factorization and of the spectral factorization for FIR data

Holger Boche; Volker Pohl

doi:10.1109/TSP.2007.906779

Robustness of the inner-outer factorization and of the spectral factorization for FIR data

Holger Boche, Volker Pohl

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

The present paper analyzes the construction of outer functions, the factorization of finite-impulse response (FIR) systems into a minimum phase system and an all-pass part, and the spectral factorization. It investigates the behavior of these operations with respect to errors in the given data. It shows that the error in the constructed outer function grows at least and at most proportional with the logarithm of the degree of the given FIR system and proportional to the error in the given data. For the other two operations, it turns out that they show the same behavior with respect to errors in the given FIR data as the construction of outer functions.

Original language	English
Pages (from-to)	274-283
Number of pages	10
Journal	IEEE Transactions on Signal Processing
Volume	56
Issue number	1
DOIs	https://doi.org/10.1109/TSP.2007.906779
State	Published - Jan 2008
Externally published	Yes

Keywords

Construction of minimum phase system
Dimensional effects
Error bounds
Inner-outer factorization
Robustness
Spectral factorization

Access to Document

10.1109/TSP.2007.906779

Cite this

@article{7604fdc409284959a07ccf08a93c5b83,

title = "Robustness of the inner-outer factorization and of the spectral factorization for FIR data",

abstract = "The present paper analyzes the construction of outer functions, the factorization of finite-impulse response (FIR) systems into a minimum phase system and an all-pass part, and the spectral factorization. It investigates the behavior of these operations with respect to errors in the given data. It shows that the error in the constructed outer function grows at least and at most proportional with the logarithm of the degree of the given FIR system and proportional to the error in the given data. For the other two operations, it turns out that they show the same behavior with respect to errors in the given FIR data as the construction of outer functions.",

keywords = "Construction of minimum phase system, Dimensional effects, Error bounds, Inner-outer factorization, Robustness, Spectral factorization",

author = "Holger Boche and Volker Pohl",

note = "Funding Information: Manuscript received March 6, 2007; revised May 31, 2007. The associate editor coordinating the review of this manuscript and approving it for publication was Dr. Vito Heloiz Nascimento. This work was partly supported by the German Research Foundation (DFG) under Grant BO 1734/11-2.",

year = "2008",

month = jan,

doi = "10.1109/TSP.2007.906779",

language = "English",

volume = "56",

pages = "274--283",

journal = "IEEE Transactions on Signal Processing",

issn = "1053-587X",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

number = "1",

}

TY - JOUR

T1 - Robustness of the inner-outer factorization and of the spectral factorization for FIR data

AU - Boche, Holger

AU - Pohl, Volker

N1 - Funding Information: Manuscript received March 6, 2007; revised May 31, 2007. The associate editor coordinating the review of this manuscript and approving it for publication was Dr. Vito Heloiz Nascimento. This work was partly supported by the German Research Foundation (DFG) under Grant BO 1734/11-2.

PY - 2008/1

Y1 - 2008/1

N2 - The present paper analyzes the construction of outer functions, the factorization of finite-impulse response (FIR) systems into a minimum phase system and an all-pass part, and the spectral factorization. It investigates the behavior of these operations with respect to errors in the given data. It shows that the error in the constructed outer function grows at least and at most proportional with the logarithm of the degree of the given FIR system and proportional to the error in the given data. For the other two operations, it turns out that they show the same behavior with respect to errors in the given FIR data as the construction of outer functions.

AB - The present paper analyzes the construction of outer functions, the factorization of finite-impulse response (FIR) systems into a minimum phase system and an all-pass part, and the spectral factorization. It investigates the behavior of these operations with respect to errors in the given data. It shows that the error in the constructed outer function grows at least and at most proportional with the logarithm of the degree of the given FIR system and proportional to the error in the given data. For the other two operations, it turns out that they show the same behavior with respect to errors in the given FIR data as the construction of outer functions.

KW - Construction of minimum phase system

KW - Dimensional effects

KW - Error bounds

KW - Inner-outer factorization

KW - Robustness

KW - Spectral factorization

UR - http://www.scopus.com/inward/record.url?scp=37749033164&partnerID=8YFLogxK

U2 - 10.1109/TSP.2007.906779

DO - 10.1109/TSP.2007.906779

M3 - Article

AN - SCOPUS:37749033164

SN - 1053-587X

VL - 56

SP - 274

EP - 283

JO - IEEE Transactions on Signal Processing

JF - IEEE Transactions on Signal Processing

IS - 1

ER -

Robustness of the inner-outer factorization and of the spectral factorization for FIR data

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this