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Estimation of rational transfer function models
Communications in Statistics - Simulation and Computation, 1984In the estimation of rational transfer function models, it has been recommended that starting values of a transfer function component be assumed to be zero (or a constant) in the recursive computation of the transfer function response. It is demonstrated that such algorithms may lead to serious bias in the estimation of moving average parameters.
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Rational functions as profile models in powder diffraction
Journal of Applied Crystallography, 1983Rational functions, the ratio of two polynomials, are shown to be good approximations to powder diffraction profiles. These functions are generalizations of the Lorentzian, the modified Lorentzian, and the profile model of Parrish [Parrish, Huang & Ayers (1976). Trans. Am. Crystallogr. Assoc. 12, 55–73]. The simplest of these functions is of the form f(
N. P. Pyrros, C. R. Hubbard
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Modeling frequency responses by positive rational functions
1991 IEEE International Symposium on Circuits and Systems (ISCAS), 1991The problem of finding a rational function of a real variable interpolating at given points (with suitable intersection numbers) while being everywhere positive is considered. The positivity requirement is essential, e.g. in modeling the square magnitude of a frequency response. This goal is achieved by resorting to a Hermite-type approach which allows
Lepschy Antonio +2 more
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Rational transfer function models for biofilm reactors
AIChE Journal, 1998AbstractDesign of controllers and optimization of plants using biofilm reactors often require dynamic models and efficient simulation methods. Standard model assumptions were used to derive nonrational transfer functions describing the fast dynamics of stirred‐tank reactors with zero‐ or first‐order reactions inside the biofilm.
Torsten Wik, Claes Breitholtz
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Modelling and Identification with Rational Orthogonal Basis Functions
IFAC Proceedings Volumes, 2000Abstract Decomposing dynamical systems in terms of orthogonal expansions enables the modelling/approximation of a system with a finite length expansion. By flexibly tuning the basis functions to underlying system characteristics, the rate of convergence of these expansions can be drastically increased, leading to highly accurate models (small bias ...
Paul Van den Hof +5 more
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Black-box modelling by rational function approximation
Proceedings. 8th IEEE Workshop on Signal Propagation on Interconnects, 2004In this paper, a rational function approach is used to approximate the transfer function of linear systems characterized by sampled data. The ill-conditioned Vandermonde-like matrix associated with the ordinary power series is avoided by using Chebyshev polynomials.
null Rong Gao +3 more
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Robust Method for Solving Rational Function Model
2010 International Conference on Electrical and Control Engineering, 2010In the past 10 years, the research on the Rational Function Model (RFM) has been a hot spot since the vendor of IKONOS high-resolution remote sensing image bring it into the commercial application. There are many points of RFM for research, but people mainly focus on how to overcom its ill-posed problem, and look for robust methods for solving the RFM.
Chen Libo, Jiao Weili
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Conflicting Specifications for Investment Functions in Rationing Models: A Reconciliation
Recherches économiques de Louvain, 1987A number of attempts have been made recently (see, a.o., Mulkay [1983], Artus and Muet [1984], Gérard and Vanden Berghe [1984]) to develop and estimate appropriate specifications for investment functions in a rationing context. Some of the specifications proposed are however clearly conflicting, not in the usual sense that they reflect conflicting ...
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The statistical properties and utility of rational functions models
The Canadian Journal of Chemical Engineering, 1987AbstractRational functions, also called “inverse polynomials”, have been used as approximations to a wide range of mathematical functions and integrals in computer applications. A fairly general rational functions model with a single regressor variable and three to five parameters, capable of fitting a wide variety of ascending and descending curves ...
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Signal Processing, 2004
We investigate in this paper how to estimate the probability density function (PDF) of a random variable using a rational parametric model for its characteristic function (CF). The choice of the model is motivated by the problem of better modeling the duration of the speech states within a hidden Markov model (HMM).
Josep Vidal +2 more
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We investigate in this paper how to estimate the probability density function (PDF) of a random variable using a rational parametric model for its characteristic function (CF). The choice of the model is motivated by the problem of better modeling the duration of the speech states within a hidden Markov model (HMM).
Josep Vidal +2 more
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