A Duality Principle for Trigonometric Wavelets J. Prestin and E. Quak

Abstract. The aim of this paper is to give a direct proof of the duality principle for decomposition and reconstruction algorithms for nested spaces of trigonometric polynomials. The scaling functions of these spaces are defined as fundamental polynomials of Lagrange interpolation. The decomposition matrix for these scaling functions and wavelets is the trans­ pose of the reconstruction matrix for the dual scaling functions and dual wavelets. Analogously, the original reconstruction matrix is the transpose of the decomposition matrix for the dual functions.