Optimum Laguerre networks for a class of discrete-time systems

Masnadi-Shirazi, Mohammad Ali; Ahmed, N.

doi:10.1109/78.134447

Cited by 85 publications

(30 citation statements)

References 5 publications

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“…Other related work concerns the Laguerre filter, also a filter structure, although different, with a restricted feedback architecture [7]. Our approach differs from previous research because filters are analyzed as short-term memory structures.…”

mentioning

confidence: 50%

“…In general, the gamma filter is preferable if the processing problem involves with energy 'Oncent rated at low frequencies and relatively few degrees of freedom. Related work has been conducted in the area of Laguerre filters where the delay operators are first-order allpass filters [7], [ll]. The work in this paper, however, takes a different viewpoint.…”

Section: Discussionmentioning

confidence: 99%

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The gamma-filter-a new class of adaptive IIR filters with restricted feedback

Prı́ncipe

Vries

Oliveira

1993

IEEE Trans. Signal Process.

129

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Abstract-In this paper we introduce the generalized feedforward filter, a new class of adaptive filters that combines attractive properties of finite impulse response (FIR) filters with some of the power of infinite impulse response (IIR) filters. A particular case, the gamma filter, generalizes Widrow's adaptive transversal filter (adaline) to an infinite impulse response filter. Yet, the stability condition for the gamma filter is trivial, and least mean square (LMS) adaptation is of the same computational complexity as the conventional transversal filter structure. Preliminary results indicate that the gamma filter is more efficient than the adaptive transversal filter. We extend the Wiener-Hopf equation to the gamma filter and develop some analysis tools.

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mentioning

confidence: 50%

Section: Discussionmentioning

confidence: 99%

The gamma-filter-a new class of adaptive IIR filters with restricted feedback

Prı́ncipe

Vries

Oliveira

1993

IEEE Trans. Signal Process.

129

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“…The first study concerning this subject which optimized the performance of Laguerre functions based models in the case of linear continuous-time systems seems to be (Clowes 1965). Later, the problem of selecting Laguerre poles in discrete-time linear systems was investigated in Masnadi-Shirazi and Ahmed (1991) by minimizing the error between the impulse response of the system and the corresponding Laguerre model. The main drawback of this strategy is that it requires finding roots of high-order polynomials.…”

Section: Introductionmentioning

confidence: 98%

An optimal expansion of Volterra models using independent Kautz bases for each kernel dimension

Rosa

Campello

Amaral

2008

International Journal of Control

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A new solution for the problem of selecting poles of the two-parameter Kautz functions in Volterra models is proposed. In general, a large number of parameters are required to represent the Volterra kernels, although this difficulty can be overcome by describing each kernel using a basis of orthonormal functions, such as the Kautz basis. This representation has a Wiener structure consisting of a linear dynamic generated by the orthonormal basis followed by a non-linear static mapping represented by the Volterra series. The resulting Wiener/Volterra model can be truncated into fewer terms if the Kautz functions are properly designed. The underlying problem is how to select the arbitrary complex poles that fully parametrize these functions. This problem has been approached in previous research by minimizing an upper bound for the error resulting from the truncation of the kernel expansion. The present paper goes even further in that each multidimensional kernel is decomposed into a set of independent Kautz bases, each of which is parametrized by an individual pair of conjugate Kautz poles intended to represent the dominant dynamic of the kernel along a particular dimension. An analytical solution for one of the Kautz parameters, valid for Volterra models of any order, is derived. A simulated example is presented to illustrate these theoretical results. The same approach is then used to model a real non-linear magnetic levitation system with oscillatory behaviour.

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“…Laguerre functions have been used in the 1950's and 1960's to represent transient signals [45], [7]. During the past decades, the use of orthogonal functions has been studied in problems of filter synthesis [22], [30] and for system identification [23], [32], [31], [6] and approximation [35], [36]. In these approaches to system identification, the input and output signals are transformed to a (Laguerre) transformed domain and standard identification techniques are applied to the signals in this domain.…”

Section: (3) K=omentioning

confidence: 99%

A generalized orthonormal basis for linear dynamical systems

Heuberger

Hof

Bosgra

Proceedings of 32nd IEEE Conference on Decision and Control

113

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Abstract-In many areas of signal, system, and control theory, orthogonal functions play an important role in issues of analysis and design. In this paper, it is shown that there exist orthogonal functions that, in a natural way, are generated by stable linear dynamical systems and that compose an orthonormal basis for the signal space e;. To this end, use is made of balanced realizations of inner transfer functions. The orthogonal functions can be considered as generalizations of, e.g., the pulse functions, Laguerre functions, and Kautz functions, and give rise to an alternative series expansion of rational transfer functions. It is shown how we can exploit these generalized basis functions to increase the speed of convergence in a series expansion, i.e., to obtain a good approximation by retaining only a finite number of expansion coefficients. Consequences for identification of expansion coefficients are analyzed, and a bound is formulated on the error that is made when approximating a system by a finite number of expansion coefficients.

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Optimum Laguerre networks for a class of discrete-time systems

Cited by 85 publications

References 5 publications

The gamma-filter-a new class of adaptive IIR filters with restricted feedback

The gamma-filter-a new class of adaptive IIR filters with restricted feedback

An optimal expansion of Volterra models using independent Kautz bases for each kernel dimension

A generalized orthonormal basis for linear dynamical systems

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