Quadrature formula for sampled functions

Khalid Minaoui (1, 2) , Thierry Chonavel (3, 1) , Benayad Nsiri (4) , Driss Aboutajdine (4)

1 SC - Département Signal et Communications
2 Lab-STICC - Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance (UMR 3192)
3 Lab-STICC_TB_CID_TOMS
4 GSCM-LRIT - Laboratoire de Recherche en Informatique et Télécommunications [Rabat]

This paper deals with efficient quadrature formulas involving functions that are observed only at fixed sampling points. The approach that we develop is derived from efficient continuous quadrature formulas, such as Gauss-Legendre or Clenshaw-Curtis quadrature. We select nodes at sampling positions that are as close as possible to those of the associated classical quadrature and we update quadrature weights accordingly. We supply the theoretical quadrature error formula for this new approach. We show on examples the potential gain of this approach.

Mots clés: Gauss-Legendre; Clenshaw-Curtis; quadrature; Peano kernel; irregular sampling.

Domaines: Traitement du signal et de l'image [eess.SP]

Khalid Minaoui, Thierry Chonavel, Benayad Nsiri, Driss Aboutajdine. Quadrature formula for sampled functions. International journal of signal processing (IJSP), 2010, 6 (2), pp.56 - 62. ⟨hal-00472689⟩