How to capture all FIR perfect reconstruction QMF banks with unimodular matrices?
Palghat P. Vaidyanathan · 2002
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.>