In this paper, a new two dimensional (2D) adaptive filter structure is developed. It is based on modeling the impulse response of the 2D IIR systems as a finite linear combination of a set of 2D Laguerre orthonormal functions. When long impulse response system is required to identify, computer simulation shows that the 2D Laguerre filter has better performance than the conventional 2D FIR filte...

We provide examples of flat Laguerre planes of Kleinewillinghöfer type E, thus completing the classification of flat Laguerre planes with respect to Laguerre translations in B. Polster and G.F. Steinke, Results Maths. (2004). These planes are obtained by a method for constructing a new flat Laguerre plane from three given Laguerre planes devised in B. Polster and G. Steinke, Canad. Math. Bull. ...

We derive the interaction Hamiltonian of a Laguerre-Gaussian beam with a simple atomic system, under the assumption of a small spread of the center of mass wave function in comparison with the waist of the Laguerre-Gaussian beam. The center of mass motion of the atomic system is taken into account. Using the properties of regular spherical harmonics the internal and center of mass coordinates a...

Laguerre geometry provides a simple approach to the design of rational curves and surfaces with rational offsets. These so-called PH curves and PN surfaces can be constructed from arbitrary rational curves or surfaces with help of a geometric transformation which describes a change between two models of Laguerre geometry. Closely related to that is their optical interpretation as anticaustics o...

We look into the nonparametric regression estimation with additive and multiplicative noise construct adaptive thresholding estimators based on Laguerre series. The proposed approach achieves asymptotically near-optimal convergence rates when unknown function belongs to Laguerre–Sobolev space. consider problem under two structures; (1) i.i.d. Gaussian errors (2) long-memory errors. In case, our...

New batch and adaptive methods are proposed to optimize the Volterra kernels expansions on a set of Laguerre functions. Each kernel is expanded on an independent Laguerre basis. The expansion coefficients, also called Fourier coefficients, are estimated in the MMSE sense or by applying the gradient technique. An analytical solution to Laguerre poles optimization is provided using the knowledge ...

We study a family of polynomials that are orthogonal with respect to the weight function e in [−1, 1], where ω ≥ 0. Since this weight function is complex-valued and, for large ω, highly oscillatory, many results in the classical theory of orthogonal polynomials do not apply. In particular, the polynomials need not exist for all values of the parameter ω, and, once they do, their roots lie in th...

Abstract. This paper discusses a method based on Laguerre polynomials combined with a Filtered Conjugate Residual (FCR) framework to compute the product of the exponential of a matrix by a vector. The method implicitly uses an expansion of the exponential function in a series of orthogonal Laguerre polynomials, much like existing methods based on Chebyshev polynomials do. Owing to the fact that...