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.

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