On the Exact Evaluation of Integrals of Wavelets

Enza Pellegrino, Chiara Sorgentone and Francesca Pitolli ()
Additional contact information
Enza Pellegrino: Department of Industrial and Information Engineering and Economics, University of L’Aquila, E. Pontieri 2, 67040 Roio Poggio, Italy
Chiara Sorgentone: Department of Basic and Applied Sciences for Engineering, Università di Roma “La Sapienza”, Via Antonio Scarpa 16, 00161 Roma, Italy
Francesca Pitolli: Department of Basic and Applied Sciences for Engineering, Università di Roma “La Sapienza”, Via Antonio Scarpa 16, 00161 Roma, Italy

Mathematics, 2023, vol. 11, issue 4, 1-13

Abstract: Wavelet expansions are a powerful tool for constructing adaptive approximations. For this reason, they find applications in a variety of fields, from signal processing to approximation theory. Wavelets are usually derived from refinable functions, which are the solution of a recursive functional equation called the refinement equation. The analytical expression of refinable functions is known in only a few cases, so if we need to evaluate refinable functions we can make use only of the refinement equation. This is also true for the evaluation of their derivatives and integrals. In this paper, we detail a procedure for computing integrals of wavelet products exactly, up to machine precision. The efficient and accurate evaluation of these integrals is particularly required for the computation of the connection coefficients in the wavelet Galerkin method. We show the effectiveness of the procedure by evaluating the integrals of pseudo-splines.

Keywords: wavelet; refinable function; refinement mask; pseudo-spline; wavelet Galerkin method; connection coefficients (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://www.mdpi.com/2227-7390/11/4/983/pdf (application/pdf)
https://www.mdpi.com/2227-7390/11/4/983/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:11:y:2023:i:4:p:983-:d:1068912

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().