In this tutorial paper we present a generalization of the transversal filter, called Laguerre filter, and study some of its more remarkable properties. This filter is obtained by replacing each delay of the transversal filter by a first order all-pass section, and by applying a first order low-pass filter (with the same pole used in the all-pass sections) to the filter’s input signal. Both the ...

This work is concerned with the optimization of Laguerre bases for the orthonormal series expansion of discrete-time Volterra models. The aim is to minimize the number of Laguerre functions associated with a given series truncation error, thus reducing the complexity of the resulting finite dimensional representation. Fu and Dumont [14] indirectly approached this problem in the context of linea...

The baryon acoustic oscillation feature can be used as a standard cosmological ruler. In practice, for sub-percent level accuracy on the distance scale, it must standardized. physical reason why is understood, so we use this to develop an algorithm which improves estimated scale. exploits fact that, over range of scales where initial correlation function well-fit by polynomial, leading order ef...

This work tackles the problem of expanding Volterra models using Laguerre functions. A strict global optimal solution is derived when each multidimensional kernel of the model is decomposed into a set of independent orthonormal bases, each of which parameterized by an individual Laguerre pole intended for representing the dominant dynamic of the kernel along a particular dimension. It is proved...

Let Ω be a symmetric cone and V the corresponding simple Euclidean Jordan algebra. In [2, 5, 6, 8] we considered the family of generalized Laguerre functions on Ω that generalize the classical Laguerre functions on R. This family forms an orthogonal basis for the subspace of L-invariant functions in L(Ω, dμν), where dμν is a certain measure on the cone and where L is the group of linear transfo...

Abstract. We use a multidimensional extension of Bailey’s transform to derive two very general q-generating functions, which are q-analogues of a paper by Exton [7]. These expressions are then specialised to give more practical formulae, which are q-analogues of generating relations for Karlssons generalised Kampe de Fériet function. A number of examples are given including q-Laguerre polynomia...