Characterization of low pass filters in a multiresolution analysis

A. San Antolín ¹

¹ Departamento de Matemáticas Universidad Autónoma de Madrid 28049 Madrid, Spain

Studia Mathematica, Tome 190 (2009) no. 2, pp. 99-116

Résumé

We characterize the low pass filters associated with scaling functions of a multiresolution analysis in a general context, where instead of the dyadic dilation one considers the dilation given by a fixed linear invertible map $A: {\mathbb R}^n\rightarrow {\mathbb R}^n$ such that $A(\mathbb Z^n) \subset \mathbb Z^n$ and all (complex) eigenvalues of $A$ have modulus greater than $1.$ This characterization involves the notion of filter multiplier of such a multiresolution analysis. Moreover, the paper contains a characterization of the measurable functions which are filter multipliers.

Détail

DOI : 10.4064/sm190-2-1

Keywords: characterize low pass filters associated scaling functions multiresolution analysis general context where instead dyadic dilation considers dilation given fixed linear invertible map mathbb rightarrow mathbb mathbb subset mathbb complex eigenvalues have modulus greater characterization involves notion filter multiplier multiresolution analysis moreover paper contains characterization measurable functions which filter multipliers