Article
Orthogonal Macroelement Scaling Vectors and Wavelets in 1-D
The Arabian Journal for Science and Engineering: Special Issue on Fractals and Wavelets
• , Vanderbilt University
• , Western Kentucky University
Publication Date
6-2-2003
We develop a {\em macroelement} based technique for constructing orthogonal univariate multiwavelets. We illustrate the technique with two examples. In the first example we provide a new construction of the symmetric, orthogonal, continuous scaling vector given in \cite{GHM}. In the second example, we construct a continuous orthogonal scaling vector with three components. The components of this scaling vector are symmetric or antisymmetric and provide approximation order 3, (equivalently, the components of $\Psi$ are orthogonal to polynomials of degree 2 or less.) We believe this second example to be new.