A new approach to spectral estimation: a tunable high-resolution spectral estimator

Byrnes, C.L.; Georgiou, Tryphon T.; Lindquist, Anders

doi:10.1109/78.875475

Cited by 161 publications

(151 citation statements)

References 19 publications

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“…Secondly, the time lags in the filter banks will decrease the accuracy. As pointed out in Byrnes et al (2000) one of the merits of the THREE algorithm is the time lag is one for all filters in the filter bank. These two effects work in different directions and which that is dominant will depend on the choice of poles for the filter banks.…”

Section: Accuracy In Estimating the State Covariancementioning

confidence: 99%

“…In Byrnes et al (2000) and Georgiou (2001) the increased precision in certain frequency ranges is emphasized, but in this example the whole frequency region is considered.…”

Section: A Numerical Examplementioning

confidence: 99%

“…The proposed algorithm resembles the THREE algorithm of Byrnes et al (2000) and they will be compared in the subsequent. Firstly, the convergence rate of the expansion coefficients is discussed.…”

Section: Comparison To the Three Algorithmmentioning

confidence: 99%

“…The algorithm uses the framework of Georgiou (2001) and is therefore closely related to the THREE algorithm proposed in Byrnes et al (2000). The mathematical foundation is given in Georgiou and Lindquist (2002).…”

Section: Introductionmentioning

confidence: 99%

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Identification of rational spectral densities using orthonormal basis functions

Blomqvist

Fanizza

2003

IFAC Proceedings Volumes

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This paper gives an algorithm for identifying spectral densities using orthonormal basis functions. Mathematically, this amounts to identifying a time-invariant linear SISO system with the additional constraint that the transfer function should be positive-real. Thus, we solve the long-standing problem of how to incorporate this positivity constraint while using orthonormal basis functions. The procedure is a variant of the THREE algorithm introduced by Byrnes, Georgiou and Lindquist. The relation between and numerical properties of the proposed and the THREE algorithms are discussed. The orthonormal basis functions are better scaled for a concentrated pole selection in the basis, which increases the accuracy of the estimates. A numerical example which highlights this phenomenon and illustrates the algorithm is given.

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Section: Accuracy In Estimating the State Covariancementioning

confidence: 99%

“…In Byrnes et al (2000) and Georgiou (2001) the increased precision in certain frequency ranges is emphasized, but in this example the whole frequency region is considered.…”

Section: A Numerical Examplementioning

confidence: 99%

Section: Comparison To the Three Algorithmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Identification of rational spectral densities using orthonormal basis functions

Blomqvist

Fanizza

2003

IFAC Proceedings Volumes

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“…We wish to estimate the spectral density Φ ∈ S m×m + of y from {y i } N i=1 . A THREE-like approach [5,19] generalizes Burglike methods in several ways. The second order statistics that are estimated from the data…”

Section: Approximation In the Itakura-saito Distancementioning

confidence: 99%

Multivariate Itakura-Saito distance for spectral estimation: Relation between time and spectral domain relative entropy rates

Ferrante

Masiero

Pavon

2012

Stochastic Systems Theory and its Applications (SSS)

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The notion of spectral relative entropy rate is defined for jointly stationary Gaussian processes. Using classical information-theoretic results, we establish a remarkable connection between time and spectral domain relative entropy rates, and therefore with a multivariate version of the classical Itakura-Saito divergence. This informationtheoretic result appears promising for applications where spectral entropy already plays an important role such as EEG analysis. It also lends support to a new spectral estimation technique recently developed by the authors where a multivariate version of the Itakura-Saito distance is employed as a spectrum divergence. A minimum complexity spectrum is provided by this new approach. Simulations suggest the effectiveness of the new technique in tackling multivariate spectral estimation tasks, especially in the case of short data records.

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On Spectral Analysis Using Models with Pre-specified Zeros

Wahlberg¹

Directions in Mathematical Systems Theory and Optimization

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A new approach to spectral estimation: a tunable high-resolution spectral estimator

Cited by 161 publications

References 19 publications

Identification of rational spectral densities using orthonormal basis functions

Identification of rational spectral densities using orthonormal basis functions

Multivariate Itakura-Saito distance for spectral estimation: Relation between time and spectral domain relative entropy rates

On Spectral Analysis Using Models with Pre-specified Zeros

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