Maple and the parameterization of orthogonal wavelet bases
The purpose of this note is educational - to illustrate with Maple the
lattice parameterization of orthogonal wavelet bases,
and to obtain parameterizations of the coefficients
of wavelet (2-channel) filter banks in terms of angles.
We will use the lattice parameterization of 2 by 2 unitary matrices.
This lattice parameterization, described by Vaidyanathan and Haong,
offers the opportunity to design orthogonal wavelet filters
via unconstrained optimization.
Maple and Matlab code:
- Maple code from the note
- parameterization of length-6 scaling filter
- parameterization of length-8 scaling filter
- parameterization of length-10 scaling filter
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