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Orthogonal Macroelement Scaling Vectors and Wavelets in 1-D
The Arabian Journal for Science and Engineering: Special Issue on Fractals and Wavelets
  • Douglas P Hardin, Vanderbilt University
  • Bruce Kessler, Western Kentucky University
Publication Date
6-2-2003
Comments

Published by The Arabian Journal for Science and Engineering: Special Issue on Fractals and Wavelets, 28:1C (2003): 73-88. http://www.kfupm.edu.sa/publications/ajse/

Abstract
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.
Citation Information
Douglas P Hardin and Bruce Kessler. "Orthogonal Macroelement Scaling Vectors and Wavelets in 1-D" The Arabian Journal for Science and Engineering: Special Issue on Fractals and Wavelets Vol. 28 Iss. 1C (2003) p. 73 - 88
Available at: http://works.bepress.com/bruce_kessler/5/