Noncausal nonminimum phase ARMA modeling of non-Gaussian processes

Athina P. Petropulu

Noncausal nonminimum phase ARMA modeling of non-Gaussian processes

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

Abstract

A method is presented for the estimation of the parameters of a noncausal nonminimum phase ARMA model for non-Gaussian random processes. Using certain higher-order cepstra slices, the Fourier phases of two intermediate sequences, h_min(n) and h_max(n), can be computed, where h_min(n) is composed of the minimum phase parts of the AR and MA models, and h_max(n) of the corresponding maximum phase parts. Under the condition that the AR and MA models do not have common zeros, these two sequences can be estimated from their phases only, and lead to the reconstruction of the AR and MA parameters, within a scalar and a time shift. The AR and MA orders do not have to be estimated separately, but they are a byproduct of the parameter estimation procedure. Unlike existing methods, the estimation procedure is fairly robust if a small order mismatch occurs. Since the robustness of the method in the presence of additive noise depends on the accuracy of the estimated phases of h_min(n) and h_max(n), the phase errors occurring due to finite length data are studied.

Original language	American English
Title of host publication	Proceedings of SPIE - The International Society for Optical Engineering
Editors	Franklin T. Luk
Publisher	Society of Photo-Optical Instrumentation Engineers
Pages	126-137
Number of pages	12
ISBN (Print)	0819416207
State	Published - 1994
Externally published	Yes
Event	Advanced Signal Processing: Algorithms, Architectures, and Implementations V - San Diego, CA, USA Duration: Jul 24 1994 → Jul 27 1994

Publication series

Name	Proceedings of SPIE - The International Society for Optical Engineering
Volume	2296

Other

Other	Advanced Signal Processing: Algorithms, Architectures, and Implementations V
City	San Diego, CA, USA
Period	7/24/94 → 7/27/94

ASJC Scopus subject areas

Electronic, Optical and Magnetic Materials
Condensed Matter Physics
Computer Science Applications
Applied Mathematics
Electrical and Electronic Engineering

Cite this

@inproceedings{d350e421adae4510bc95164cabc8701f,

title = "Noncausal nonminimum phase ARMA modeling of non-Gaussian processes",

abstract = "A method is presented for the estimation of the parameters of a noncausal nonminimum phase ARMA model for non-Gaussian random processes. Using certain higher-order cepstra slices, the Fourier phases of two intermediate sequences, hmin(n) and hmax(n), can be computed, where hmin(n) is composed of the minimum phase parts of the AR and MA models, and hmax(n) of the corresponding maximum phase parts. Under the condition that the AR and MA models do not have common zeros, these two sequences can be estimated from their phases only, and lead to the reconstruction of the AR and MA parameters, within a scalar and a time shift. The AR and MA orders do not have to be estimated separately, but they are a byproduct of the parameter estimation procedure. Unlike existing methods, the estimation procedure is fairly robust if a small order mismatch occurs. Since the robustness of the method in the presence of additive noise depends on the accuracy of the estimated phases of hmin(n) and hmax(n), the phase errors occurring due to finite length data are studied.",

author = "Petropulu, {Athina P.}",

year = "1994",

language = "American English",

isbn = "0819416207",

series = "Proceedings of SPIE - The International Society for Optical Engineering",

publisher = "Society of Photo-Optical Instrumentation Engineers",

pages = "126--137",

editor = "Luk, {Franklin T.}",

booktitle = "Proceedings of SPIE - The International Society for Optical Engineering",

note = "Advanced Signal Processing: Algorithms, Architectures, and Implementations V ; Conference date: 24-07-1994 Through 27-07-1994",

}

Petropulu, AP 1994, Noncausal nonminimum phase ARMA modeling of non-Gaussian processes. in FT Luk (ed.), Proceedings of SPIE - The International Society for Optical Engineering. Proceedings of SPIE - The International Society for Optical Engineering, vol. 2296, Society of Photo-Optical Instrumentation Engineers, pp. 126-137, Advanced Signal Processing: Algorithms, Architectures, and Implementations V, San Diego, CA, USA, 7/24/94.

Noncausal nonminimum phase ARMA modeling of non-Gaussian processes. / Petropulu, Athina P.
Proceedings of SPIE - The International Society for Optical Engineering. ed. / Franklin T. Luk. Society of Photo-Optical Instrumentation Engineers, 1994. p. 126-137 (Proceedings of SPIE - The International Society for Optical Engineering; Vol. 2296).

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

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PY - 1994

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N2 - A method is presented for the estimation of the parameters of a noncausal nonminimum phase ARMA model for non-Gaussian random processes. Using certain higher-order cepstra slices, the Fourier phases of two intermediate sequences, hmin(n) and hmax(n), can be computed, where hmin(n) is composed of the minimum phase parts of the AR and MA models, and hmax(n) of the corresponding maximum phase parts. Under the condition that the AR and MA models do not have common zeros, these two sequences can be estimated from their phases only, and lead to the reconstruction of the AR and MA parameters, within a scalar and a time shift. The AR and MA orders do not have to be estimated separately, but they are a byproduct of the parameter estimation procedure. Unlike existing methods, the estimation procedure is fairly robust if a small order mismatch occurs. Since the robustness of the method in the presence of additive noise depends on the accuracy of the estimated phases of hmin(n) and hmax(n), the phase errors occurring due to finite length data are studied.

AB - A method is presented for the estimation of the parameters of a noncausal nonminimum phase ARMA model for non-Gaussian random processes. Using certain higher-order cepstra slices, the Fourier phases of two intermediate sequences, hmin(n) and hmax(n), can be computed, where hmin(n) is composed of the minimum phase parts of the AR and MA models, and hmax(n) of the corresponding maximum phase parts. Under the condition that the AR and MA models do not have common zeros, these two sequences can be estimated from their phases only, and lead to the reconstruction of the AR and MA parameters, within a scalar and a time shift. The AR and MA orders do not have to be estimated separately, but they are a byproduct of the parameter estimation procedure. Unlike existing methods, the estimation procedure is fairly robust if a small order mismatch occurs. Since the robustness of the method in the presence of additive noise depends on the accuracy of the estimated phases of hmin(n) and hmax(n), the phase errors occurring due to finite length data are studied.

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M3 - Conference contribution

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T3 - Proceedings of SPIE - The International Society for Optical Engineering

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BT - Proceedings of SPIE - The International Society for Optical Engineering

A2 - Luk, Franklin T.

PB - Society of Photo-Optical Instrumentation Engineers

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ER -

Noncausal nonminimum phase ARMA modeling of non-Gaussian processes

Abstract

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ASJC Scopus subject areas

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