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Design of interpolating biorthogonal multiwavelet systems with compact support. (English) Zbl 1010.42018

The paper presents a framework for the construction of totally interpolating multiwavelet systems of multiplicity \(2\), that is, each multiscaling function and each multiwavelet in this orthogonal system has the interpolating property.
While such multiwavelet systems can be designed with arbitrary approximation order, it can be shown that totally interpolating biorthogonal filter banks can not be symmetric.
Examples with approximation order two and three are provided. The interpolation properties imply equality between the uniform samples of a signal and its projection coefficients for a given scale, such that the usual prefiltering associated with standard multiwavelet systems can be avoided.

MSC:

42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
41A05 Interpolation in approximation theory
65D05 Numerical interpolation
65T60 Numerical methods for wavelets
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