Matrix Extension with Symmetry and Its Application to Filter Banks. (arXiv:1001.1117v1 [cs.IT])

In this paper, we completely solve the matrix extension problem with symmetry
and provide a step-by-step algorithm to construct such a desired matrix
$mathsf{P}_e$ from a given matrix $mathsf{P}$. Furthermore, using a cascade
structure, we obtain a complete representation of any $r imes s$ paraunitary
matrix $mathsf{P}$ having compatible symmetry, which in turn leads to an
algorithm for deriving a desired matrix $mathsf{P}_e$ from a given matrix
$mathsf{P}$. Matrix extension plays an important role in many areas such as
electronic engineering, system sciences, applied mathematics, and pure
mathematics. As an application of our general results on matrix extension with
symmetry, we obtain a satisfactory algorithm for constructing symmetric
paraunitary filter banks and symmetric orthonormal multiwavelets by deriving
high-pass filters with symmetry from any given low-pass filters with symmetry.
Several examples are provided to illustrate the proposed algorithms and results
in this paper.

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Original source : http://arxiv.org/abs/1001.1117...