How to capture all FIR perfect reconstruction QMF banks with unimodular matrices?

The problem of perfect reconstruction in maximally decimated FIR (finite impulse response) QMF (quadrature mirror filter) banks is revisited. A necessary and sufficient condition for perfect reconstruction in this system is that the polyphase matrix of the analysis bank must have a determinant equal to a delay. The author explores various avenues to completely parameterize such matrices. It is shown that the problem can always be decomposed into two problems: one of parameterizing lossless matrices, and one of parameterizing unimodular matrices. Several possibilities for unimodular parameterization are explored.<<ETX>>

[1]  E. Viscito,et al.  Design of perfect reconstruction multi-dimensional filter banks using cascaded Smith form matrices , 1988, 1988., IEEE International Symposium on Circuits and Systems.

[2]  Martin Vetterli,et al.  Perfect reconstruction FIR filter banks: some properties and factorizations , 1989, IEEE Trans. Acoust. Speech Signal Process..

[3]  Thomas Kailath,et al.  Linear Systems , 1980 .

[4]  David W. Lewis,et al.  Matrix theory , 1991 .

[5]  P. P. Vaidyanathan,et al.  The role of lossless systems in modern digital signal processing: a tutorial , 1989 .

[6]  Martin Vetterli,et al.  A theory of multirate filter banks , 1987, IEEE Trans. Acoust. Speech Signal Process..

[7]  Mark J. T. Smith,et al.  Exact reconstruction techniques for tree-structured subband coders , 1986, IEEE Trans. Acoust. Speech Signal Process..

[8]  R. Kálmán.  Irreducible realizations and the degree of a rational matrix. , 1965 .

[9]  Truong Q. Nguyen,et al.  General synthesis procedures for FIR lossless transfer matrices, for perfect-reconstruction multirate filter bank applications , 1988, IEEE Trans. Acoust. Speech Signal Process..

[10]  P. Vaidyanathan.  Quadrature mirror filter banks, M-band extensions and perfect-reconstruction techniques , 1987, IEEE ASSP Magazine.

[11]  P. P. Vaidyanathan,et al.  Theory and design of M-channel maximally decimated quadrature mirror filters with arbitrary M, having the perfect-reconstruction property , 1987, IEEE Trans. Acoust. Speech Signal Process..

[12]  P. P. Vaidyanathan,et al.  Multirate digital filters, filter banks, polyphase networks, and applications: a tutorial , 1990, Proc. IEEE.