Stability and Independence of the Shifts of Finitely Many Refinable Functions.
Abstract
Typical constructions of wavelets depend on the stability of the shifts of an underlying refinable function. Unfortunately, several desirable properties are not available with compactly supported orthogonal wavelets, e.g. symmetry and piecewise polynomial structure. Presently, multiwavelets seem to offer a satisfactory alternative. The study of multiwavelets involves the consideration of the properties of several (simultaneously) refinable functions. In Section 2 of this paper, we characterize stability and linear independence of the shifts of a finite refinable function set in terms of the refinement mask. Several illustrative examples are provided. The characterizations given in Section 2 actually require that the refinable functions be minimal in some sense. This notion of minimality is made clear in Section 3, where we provide sufficient conditions on the mask to ensure minimality. The conditions are shown to be also necessary under further assumptions on the refinement mask. An example is provided illustrating how the software package MAPLE can be used to investigate at least the case of two simultaneously refinable functions.
Document Details
- Document Type
- Technical Report
- Publication Date
- Feb 01, 1996
- Accession Number
- ADA304489
Entities
People
- Thomas A. Hogan
Organizations
- University of Wisconsin–Madison