Discrete biorthogonal wavelets and PR finite impulse response (FIR) filter banks via block circulant matrices
Jaroslav Kautský, Radka Turcajová · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1994
Factorization of orthogonal block circulant matrices can not be generalized in a straightforward way for block circulant matrices which are merely invertible. However, they can be decomposed into an orthogonal matrix and an atom that represents the `nonorthogonal' part of the matrix. Atoms can be characterized by nilpotent block-companion matrices. This characterization permits, for example, to derive bounds for the width of the band of the inverse of a banded block circulant matrix.