Suppose a real-valued function φ ∈ L2(R) satisfies the following conditions: (a) φ̂(2ω) = m0(ω)φ̂(ω), where m0 is an essentially bounded 2π -periodic function; and (b) limω→0 φ̂(ω) = (2π)−1/2; then the function φ is called refinable or scaling, m0 is called a symbol of φ, and the relation in item (a) is called a refinement equation. Every refinable function generates multiresolution analysis (MRA)...

The theory of wavelets and multiresolution analysis is usually developed on R. However, applications of wavelets to image processing and numerical methods for partial differential equations require multiresolution analysis on domains or manifolds in R. The study of multiresolution in these settings is just beginning. Building on the construction of multiresolution on intervals (and cubes in R )...

In this paper we explore the use of features derived from multiresolution analysis of speech and the Teager Energy Operator for classi cation of drivers' speech under stressed conditions. We apply this set of features to a database of short speech utterances to create userdependent discriminants of four stress categories. In addition we address the problem of choosing a suitable temporal scale ...

The purpose of this paper is to study the relationships between the support of a reenable distribution and the global and local linear independence of the integer translates of : It has been shown elsewhere that a compactly supported distribution has globally independent integer translates if and only if has minimal convex support. However, such a distribution may have \holes" in its support. B...

We introduce a new approach in order to construct a wavelets with arbitrary support on the interval. This result allows us to adapt on the interval some important classes of wavelets (coiflets, symlets, Lemarié's wavelets). In addition, we show how to obtain multiresolution analysis on the interval with better approximation rate in some neighborhood of the interval.

We improve Wang's characterization for a pair of biorthogonal wavelets to be associated with biorthogonal multiresolution analyses (MRA's). We show that one of the two conditions in his characterization is redundant, and, along the way, show that for a pair of biorthogonal wavelets to be associated with biorthogonal MRA's it is necessary and suÆcient that one of the wavelets is associated with ...