Alfredo Eisinberg

Fast communication: A Prony-like method for non-uniform sampling

In this paper a Prony-like method for non-uniform sampling is proposed. The unknown parameters are estimated on the base of a new linear regression equation which uses filtered signals obtained directly from the measurements. The approach uses the derivative method in the frequency domain yielding exact formula in terms of multiple integrals of the signal, when placed in the time domain. These integrals are explicitly solved by projecting signal on some set of orthogonal basis functions or, more in general, by using a polynomial that fits data in the least-squares sense. The effectiveness of the proposed approach is shown by simulated experiments.

A property of the elementary symmetric functions on the frequencies of sinusoidal signals

In this paper, a relation between the elementary symmetric functions on the frequencies of multi-sine wave signal and its multiple integrals is proposed. The approach used herein is based on the algebraic derivative method in the frequency domain, which allows to yield exact formula in terms of multiple integrals of the signal when placed in the time domain. Moreover, it allows to free oneself from the hypothesis of uniform sampling. Two different ways to approach the estimation are advised, the first is based on least-squares estimation, while the second one is based on the solution of a linear system of dimension equal to the number of sinusoidal components involved. For an easy time realization of such formula, a time-varying filter is proposed. Due to use of multiple integrals of the signal, the resulting parameters estimation is accurate in the face of large measurement noise. To corroborate the theoretical analysis and to investigate the performance of the developed algorithm, computer simulated and laboratory experiments data records are processed.

Modulating functions method plus SOGI scheme for signal tracking

The number of equipments based on static converters such as uninterrupted power systems, series or shunt compensators and distributed generations systems is increasing in the actual power distribution systems. For a correct operation in grid connected condition, these equipments need the information about amplitude, phase angle and frequency of the grid fundamental voltages and currents. Since noise as harmonic pollution and frequency variations are common problems in the utility grid, then it is necessary to have systems able to extract information about the fundamental values from highly distorted signals. For these reasons, robust and accurate estimation and synchronization methods are necessary to obtain the above information also in noise environmental. In this paper, a simple and robust method for frequency estimation based on modulating functions is presented; moreover it is used in addition to an orthogonal system generation method based on the second order generalized integrator (SOGI). The combined use of the two methods has the advantages of a fast and accurate signal tracking capabilities and a good rejection to noise due to the low-pass filter properties of the modulating functions. The effectiveness of the proposed method is validated through simulated experiments and comparisons.

Vandermonde systems on equidistant nodes in [0,1]: accurate computation

This paper deals with Vandermonde matrices V whose nodes are the equidistant points in [0,1]. We give an analytic factorization and explicit formula for the entries of their inverse, and explore its computational issues. We also give asymptotic estimates of the Frobenius norm of both V and its inverse and show that a new representation of the floating point number system allows one to build an accurate algorithm for the interpolation problem on equidistant nodes in [0,1].

Vandermonde systems on Gauss-Lobatto Chebyshev nodes

Abstract This paper deals with Vandermonde matrices V n whose nodes are the Gauss–Lobatto Chebyshev nodes, also called extrema Chebyshev nodes. We give an analytic factorization and explicit formula for the entries of their inverse, and explore its computational issues. We also give asymptotic estimates of the Frobenius norm of both V n and its inverse and present an explicit formula for the determinant of V n .

Discrete orthogonal polynomials on Gauss--Lobatto Chebyshev nodes

In this paper, we present explicit formulas for discrete orthogonal polynomials over the so-called Gauss-Lobatto Chebyshev points. In particular, this allows us to compute the coefficient in the three-terms recurrence relation and the explicit formulas for the discrete inner product. The paper also contains numerical examples related to the least-squares problems.

On an integral representation of a class of Kapteyn (Fourier―Bessel) series: Kepler's equation, radiation problems and Meissel's expansion

Abstract In this paper, an integral representation of a class of Kapteyn series is proposed. Such a representation includes the most used series in practical applications. The approach uses the property of uniform convergence of the considered class and the integral representation of the Bessel functions. The usefulness of the proposed method is highlighted by providing an integral solution of Kepler’s equation and of some Kapteyn series arising in radiation problems. Moreover it allows us to generalize a result due to Meissel.

Accurate floating-point summation: a new approach

The aim of this paper is to find an accurate and efficient algorithm for evaluating the summation of large sets of floating-point numbers. We present a new representation of the floating-point number system in which a number is represented as a linear combination of integers and the coefficients are powers of the base of the floating-point system. The approach allows to build up an accurate floating-point summation algorithm based on the fact that no rounding error occurs whenever two integer numbers are summed or a floating-point number is multiplied by powers of the base of the floating-point system. The proposed algorithm seems to be competitive in terms of computational effort and, under some assumptions, the computed sum is greatly accurate. With such assumptions, less-conservative in the practical applications, we prove that the relative error of the computed sum is bounded by the unit roundoff.

Lebesgue constant for Lagrange interpolation on equidistant nodes

Properties of Lebesgue function for Lagrange interpolation on equidistant nodes are investigated. It is proved that Lebesgue function can be formulated both in terms of a hypergeometric function,2F1 and Jacobi polynomials. Moreover, an integral expression of Lebesgue function is also obtained and the asymptotic behavior of Lebesgue constant is studied.

An analytic optimization procedure to estimate a first-order plus time delay model from step response

In this paper an identification method to estimate the parameters of a first order plus time delay model is proposed. Such a method directly obtains these parameters using a filtered equation and an optimization procedure without iterative calculations. A simple true/false criterion to establish if the hypothesis on the process type is correct can be easily derived. The proposed method shows an acceptable robustness to disturbances and measurement noise as it is confirmed by several simulated experiments.