A Newton-Raphson method for moving-average spectral factorization using the Euclid algorithm

Demeure, C.J.; Mullis, C.T.

doi:10.1109/29.60101

Cited by 36 publications

(11 citation statements)

References 14 publications

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“…However, this method is not recommended due the numerical instabilities associated with root finding. Other methods, such as [19], which find minimum-phase spectral factors without explicitly computing the root locations, exist.…”

Section: B Spectral-domain Subband Mmse Analysismentioning

confidence: 99%

“…However, the inverse Fourier transform of (18) will not necessarily correspond to a causal sequence. Because the optimal FIR adaptive solution is a special case of noncausal adaptive filters (19) 2) Infinite Causal Case: With causal constraints, the solution can be found by constructing a model to synthesize and such that they have the appropriate spectral densities. This modeling technique is described in [18].…”

Section: B Spectral-domain Subband Mmse Analysismentioning

confidence: 99%

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Mean square error analysis of nonuniform subband adaptive filters for system modeling

Griesbach

Lightner²,

Etter³

2005

IEEE Trans. Signal Process.

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Nonuniform filterbanks have recently been proposed for subband adaptive filters (SAFs). However, nonuniform SAFs have not yet been given a thorough performance analysis. This paper gives a comprehensive mean square error (MSE) analysis of system modeling, nonuniform (and, degeneratively, uniform) SAFs after convergence for a specified filterbank. Using the equivalent polyphase representation suggested by Ono et al., minimum MSE (MMSE) estimates for the individual subband errors are presented with respect to a given filterbank for finite length (FIR), infinite length causal (IIR), and infinite noncausal adaptive filters. Using these subband MMSE estimators, an MMSE estimator is derived for the overall fullband error. Finally, the derived MMSE estimators are verified by a numerical simulation. The intent of this paper is not to compare nonuniform and uniform SAF performance but merely to present a unified mathematical methodology to predict their MMSEs.

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Section: B Spectral-domain Subband Mmse Analysismentioning

confidence: 99%

Section: B Spectral-domain Subband Mmse Analysismentioning

confidence: 99%

Mean square error analysis of nonuniform subband adaptive filters for system modeling

Griesbach

Lightner²,

Etter³

2005

IEEE Trans. Signal Process.

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“…v i x i of degrees k and l = n − k, respectively, served as a basis for effective root-finding algorithms in [54,16,17], but it also represents deflation, that is polynomial division with no remainder and is of independent interest due to its applications to the time series analysis, Weiner filtering, noise variance estimation, covariance matrix computation, and the study of multi-channel systems [65][66][67][68][69][70]. The factorization can be equivalently expressed by any of the two following vector equations (cf., e.g., [73,74]),…”

Section: Numerical Factorization Of a Polynomialmentioning

confidence: 99%

New progress in real and complex polynomial root-finding

Pan

Zheng

2011

Computers & Mathematics with Applications

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a b s t r a c tMatrix methods are increasingly popular for polynomial root-finding. The idea is to approximate the roots as the eigenvalues of the companion or generalized companion matrix associated with an input polynomial. The algorithms also solve secular equation. QR algorithm is the most customary method for eigen-solving, but we explore the inverse Rayleigh quotient iteration instead, which turns out to be competitive with the most popular root-finders because of its excellence in exploiting matrix structure. To advance the iteration we preprocess the matrix and incorporate Newton's linearization, repeated squaring, homotopy continuation techniques, and some heuristics. The resulting algorithms accelerate the known numerical root-finders for univariate polynomial and secular equations, and are particularly well suited for the acceleration by using parallel processing. Furthermore, even on serial computers the acceleration is dramatic for numerical approximation of the real roots in the typical case where they are much less numerous than all complex roots.

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“…and [8], the classical problem of spectral factorization is addressed using a NewtonRaphson algorithm. By enforcing symmetry, a special Euclidian algorithm with some remarkable propertis emerges.…”

Section: Abstract (Maximum 200 Words)mentioning

confidence: 99%

Algorithms and Structures for Real-Time Signal Processing. Revised

Mullis¹

1994

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A Newton-Raphson method for moving-average spectral factorization using the Euclid algorithm

Cited by 36 publications

References 14 publications

Mean square error analysis of nonuniform subband adaptive filters for system modeling

Mean square error analysis of nonuniform subband adaptive filters for system modeling

New progress in real and complex polynomial root-finding

Algorithms and Structures for Real-Time Signal Processing. Revised

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