Balanced realizations of discrete-time stable all-pass systems and the tangential Schur algorithm

Hanzon, Bernard; Olivi, Martine; Peeters, Ralf

doi:10.1016/j.laa.2006.03.027

Cited by 22 publications

(48 citation statements)

References 19 publications

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“…In the context of SAW filters, the Schur algorithm associated with the matrices Φ n has a nice physical interpretation: it gives the sequence of acoustic matrices M n corresponding to the first n-cells of the filter. Moreover, it can be proved that it allows for a recursive construction of balanced realizations as described in [8]. This is not very surprising since, when the interpolation point w is zero, the choices in [10] and [8] for the matrix Θ agree.…”

Section: Consider the Matrixmentioning

confidence: 84%

“…Recall that a linear fractional transformation T H associated with such a J-unitary matrix H is a bijection on the set of inner functions which preserves the McMillan degree [8]. Moreover, if Θ is a J-inner function, we have that…”

Section: Parametrizationmentioning

confidence: 99%

“…This choice naturally arises in a function space approach [4]. The matrix Θ w,u,v also has the nice factorization (obtained from [8,Lemma 5…”

Section: Parametrizationmentioning

confidence: 99%

“…It is described in the case of continuous-time transfer functions, but it corresponds in our discrete-time setting to the choice of Θ w,u,v H(vu * ) −1 . In [8], the freedom in the choice of the matrix H has been used to associate with the Schur algorithm a nice recursive construction of balanced realizations. This is possible with the J-inner matrix…”

Section: Parametrizationmentioning

confidence: 99%

“…This leads us to some considerations on the choice of the J-inner function in a Schur algorithm. Concerning the tangential Schur algorithm described in section II, we have already mentioned that several choices have been made in the literature (see remark 1) and in particular, that of [10] which allows for a nice circuit interpretation, and that of [8] which leads to a recursive construction of balanced realizations. In the context of SAW filters, the Schur algorithm associated with the matrices Φ n has a nice physical interpretation: it gives the sequence of acoustic matrices M n corresponding to the first n-cells of the filter.…”

Section: Consider the Matrixmentioning

confidence: 99%

See 4 more Smart Citations

A Schur algorithm for symmetric inner functions.

Olivi

Hanzon

Peeters

Proceedings of the 44th IEEE Conference on Decision and Control

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Symmetric inner rational functions naturally arise in the description of physical systems which satisfy the conservation and reciprocity laws. Inner matrix functions can be parametrized by a sequence of interpolation vectors obtained from a tangential Schur algorithm. In this paper, we present a Schur type algorithm which allows to describe symmetric inner functions, based on a two-sided Nudelman interpolation problem. This Schur algorithm gives rise to an interesting interpretation in the context of surface acoustic wave filters.

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Section: Consider the Matrixmentioning

confidence: 84%

Section: Parametrizationmentioning

confidence: 99%

“…This choice naturally arises in a function space approach [4]. The matrix Θ w,u,v also has the nice factorization (obtained from [8,Lemma 5…”

Section: Parametrizationmentioning

confidence: 99%

Section: Parametrizationmentioning

confidence: 99%

Section: Consider the Matrixmentioning

confidence: 99%

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A Schur algorithm for symmetric inner functions.

Olivi

Hanzon

Peeters

Proceedings of the 44th IEEE Conference on Decision and Control

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Orthogonal Matched Wavelets with Vanishing Moments: A Sparsity Design Approach

Karel

Peeters

2017

Circuits Syst Signal Process

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This paper presents a novel approach to design orthogonal wavelets matched to a signal with compact support and vanishing moments. It provides a systematic and versatile framework for matching an orthogonal wavelet to a specific signal or application. The central idea is to select a wavelet by optimizing a criterion which promotes sparsity of the wavelet representation of a prototype signal. Optimization is performed over the space of orthogonal wavelet functions with compact support, coming from filter banks with a given order. Parametrizations of this space are accompanied by explicit conditions for extra vanishing moments, to be used for constrained optimization. The approach is developed first for critically sampled wavelet transforms, then for undecimated wavelet transforms. Two different optimization criteria are presented: to achieve sparsity by L 1 -minimization or by L 4 -norm maximization. Masking can be employed by introducing weighting factors. Examples are given to demonstrate and evaluate the approach.

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Nudelman interpolation, parametrizations of lossless functions and balanced realizations

Marmorat¹,

Olivi

2007

Automatica

Self Cite

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We investigate the parametrization issue for discrete-time stable allpass multivariable systems by means of a Schur algorithm involving a Nudelman interpolation condition. A recursive construction of balanced realizations is associated with it, that possesses a very good numerical behavior. Several atlases of charts or families of local parametrizations are presented and for each atlas a chart selection strategy is proposed. The last one can be viewed as a nice mutual encoding property of lossless functions and turns out to be very efficient. These parametrizations allow for solving optimization problems within the fields of system identification and optimal control.

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Balanced realizations of discrete-time stable all-pass systems and the tangential Schur algorithm

Cited by 22 publications

References 19 publications

A Schur algorithm for symmetric inner functions.

A Schur algorithm for symmetric inner functions.

Orthogonal Matched Wavelets with Vanishing Moments: A Sparsity Design Approach

Nudelman interpolation, parametrizations of lossless functions and balanced realizations

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