Léon-Claude Calvez

Online optimization of the time scale in adaptive Laguerre-based filters

A new online method to optimize the free parameter in adaptive Laguerre-based filters is presented, it is based on the minimization of a criterion that is equivalent to an upper bound for the quadratic approximation error. The proposed technique presents a fast convergence and a good robustness.

Optimum choice of free parameter in orthonormal approximations

This correspondence investigates the choice of a free parameter, usually related to time scale, that minimizes the error energy when approximating a given signal with some widely used orthonormal basis functions. The proposed solution is the best that can be achieved with the limited required knowledge of the signal. It is appealing for experimental data for which no exact mathematical expression is available. >

Pertinent choice of parameters for discrete Kautz approximation

Kautz functions have received much attention in the recent mathematical modeling and identification literature. These functions which involve free parameters can approximate efficiently signals with strong oscillatory behavior. We consider here the choice of the free parameters in discrete (two-parameter) Kautz approximation. Using a key relationship between Kautz and Laguerre expansions we derive an upper bound for the quadratic truncation error. Minimization of this upper bound yields pertinent parameters, whose computation then requires reduced knowledge of the function to be modeled.

Laguerre-Gram reduced-order modeling

We present an efficient model reduction procedure based on the Laguerre description of the system to be approximated. Using a one-order operator defined in the Laplace domain we construct a pencil of functions and formulate the problem as the minimization of the L/sub /spl infin///sup 2/(/spl Ropf//sup +/) criterion. The use of a weight function in the inner product definition allows a control of the time-error spreading in model reduction procedure. We show how the required Gram matrix can be computed efficiently and prove that the impulse response of the reduced model is also in L/sub /spl infin///sup 2/(/spl Ropf//sup +/). The transfer function approach allows an immediate and promising application in model reduction of infinite dimensional systems. An extension to multiple-input-multiple-output systems is also given.

Improved method for optimum choice of free parameter in orthogonal approximations

We report on our investigations to choose a free parameter to minimize the error energy when approximating a given signal with orthogonal basis functions. This method requires limited knowledge of the signal to be approximated and has a low computational cost.

A new discrete impulse response Gramian and its application to model reduction

Some fundamental properties of an impulse response Gramian for linear, time-invariant, asymptotically stable, discrete single-input-single-output (SISO) systems are derived. This Gramian is system invariant and can be found by solving a Lyapunov equation. The connection with standard controllability, observability, and cross Gramians is proven. The significance of these results in model-order reduction is highlighted with an efficient procedure.

Low Complexity Equivalent Circuit Models for VLSI Interconnects

In this paper we present a technique for generating low complexity equivalent circuit models for VLSI circuit interconnects via the Laguerre-Gram model order reduction (MOR) method developed by our team. We discuss model passivity and equivalent circuit implementation and then show the advantages of our method in preserving important signal parameters such as rise time, delay and overshoot

Gram matrix of a Laguerre model: application to model reduction of irrational transfer function

An efficient method for evaluating inner products of repeated integrals and derivatives of a function described by a Laguerre model is presented. An immediate and promising application is model reduction of infinite-dimensional transfer functions.

A frequency domain approach for efficient model reduction of mixed VLSI circuits

It has become well accepted that interconnect delay dominates gate delay in current VLSI circuits. This paper introduces a new method, based on a frequency domain approach, for the simulation of interconnect problems found in high speed digital circuits and SOC-AMS.

Balanced Realization using an Orthogonalization Procedure and Modular Polynomial Arithmetic

A new procedure for deriving a balanced realization of continuous time or discrete time block-factorized transfer function is proposed. This work is based on orthogonalization processes of input maps through use of Routh\Astrom tables and modular polynomial arithmetic.