Rational Approximation of Transfer Functions for Non-Negative EPT Densities

Conor Sexton (1) , Martine Olivi (2) , Bernard Hanzon (1)

1 School of Mathematical Sciences [Cork]
2 APICS - Analysis and Problems of Inverse type in Control and Signal processing

An Exponential-Polynomial-Trigonometric (EPT) function is defined on [0,∞) by a minimal realization (A, b, c). A stable non-negative EPT function of a fixed degree is fitted to the histogram of a large set of data using an L2 criterion. If we neglect the non-negativity constraint this is shown to be equivalent to a rational approximation problem which is approached using the RARL2 software. We show how, under the additional assumption of the existence of a strictly dominant real pole of the rational function, the non-negativity constraint on the EPT function can be imposed by performing a constraint convex optimization on b at each stage at which an (A, c) pair is determined. In this convex optimization step a recent generalized Budan-Fourier sequence approach to determine non-negativity of an EPT function on a finite interval plays a major role.

Mots clés: Probability Density Function; Rational Matrices; Fourier Transforms; Impulse Responses; Lyapunov Function; Convex Optimisationl; Function Approximation; Sampled Data; Financial Systems

Domaines: Optimisation et contrôle [math.OC]

Conor Sexton, Martine Olivi, Bernard Hanzon. Rational Approximation of Transfer Functions for Non-Negative EPT Densities. 16th IFAC Symposium on System Identification, Jul 2012, Bruxelles, Belgium. pp.716-721, ⟨10.3182/20120711-3-BE-2027.00197⟩. ⟨hal-00763205⟩