The present paper is devoted to a systematic study of the combinatorial interpretations of the moments and the linearization coefficients of the orthogonal Sheffer polynomials, i.e., Hermite, Charlier, Laguerre, Meixner and Meixner-Pollaczek polynomials. In particular, we show that Viennot's combinatorial interpretations of the moments can be derived directly from their classical analytical exp...

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 investigate Wiener filtering of wavelet coefficients for signal denoising. Empirically designed wavelet-domain Wiener filters have superior performance over other denoising algorithms using wavelet thresholding. However, it is not clear how we should choose the signal model that is used to design the filter, because the effect of model selection on the filter performance was hard to understa...

In this paper, we consider the partition function of a Laguerre type random matrix model

In this paper the Laguerre geometry of three-dimensional Galilei space, that is, the geometry of oriented planes and cycles of an aane Cayley-Klein space with absolute line and two conjugate complex absolute points on it, is studied. Several diierent models are presented: A cyclographic model and an isotropic model together with their duals and an interpretation in terms of geometrical optics o...

Polster and Steinke [Result. Math., 46 (2004), 103–122] determined the possible Kleinewillinghöfer types of flat Laguerre planes. These types reflect transitivity properties of groups of certain central automorphisms. We exclude three more types from the list given there with respect to Laguerre homotheties. This yields a complete determination of all possible single types with respect to Lague...

The identification algorithm of Wiener-Hammerstein nonlinear model is proposed in the paper. When the nonlinearity in the Wiener-Hammerstein model is approximated by polynomial or spline function, the identification algorithms can be implemented iteratively, and the compensator for the nonlinear distortion is given by using the estimated Wiener-Hammerstein model and its inverse. A numerical sim...

In this paper, a new LQG control design based on input-output data for linear time invariant continuous-time systems is proposed. Considering the laguerre series expansion of input-output signals, the controller can be synthesized using only the coefficients by an algebraic calculation. The analysis of the system transformed by the laguerre series expansion is utilized to lead this design metho...

The main object of this paper is to give a di erent approach to proof of generating matrix functions for Laguerre matrix polynomials. We also obtain the hypergeometric matrix representations, addition theorem, nite summation formula and an integral representation for Laguerre matrix polynomials. We get the relations between Laguerre, Legendre and Hermite matrix polynomials. We get the generatin...