Oversampled linear-phase perfect reconstruction filterbanks: theory, lattice structure and parameterization

The paper presents the theory, lattice structure, and parameterization for a general class of P-channel oversampled linear-phase perfect reconstruction filterbanks (OLPPRFBs) - systems with sampling factor M (P/spl ges/M) and filter length of L=KM (K/spl ges/1) each. For these OLPPRFBs, the necessary existence conditions on the number of symmetric filters, n/sub /spl beta//, and antisymmetric filters, n/sub /spl alpha//, (i.e., symmetry polarity) are first investigated. VLSI-friendly lattice structures are then developed for two types of OLPPRFBs, type I system (n/sub /spl beta//=n/sub /spl alpha//) and type II system (n/sub /spl beta///spl ne/n/sub /spl alpha//). The completeness and minimality of each type of lattice are also analyzed. Compared with existing work, the proposed lattices are the most general and efficient ones for OLPPRFBs. Besides, through the lattice structures, the sufficiency of the existence conditions is also verified. Next, lifting-based structures are proposed to parameterize a left invertible matrix and all of its left inverses, which leads to unconstrained optimization as well as robust implementation of OLPPRFBs. Finally, several design examples are presented to confirm the validity of the theory and demonstrate the versatility of synthesis filterbanks in the oversampled system.