Generalized Lapped Pseudo Biorthogonal Transforms

We investigate a special class of N-channel oversampled linearphase perfect reconstruction filter banks with a smaller decimation factor M than N. We deal with systems in which all analysis and synthesis filters have the same FIR length and share the same center of symmetry. We provide the general lattice factorization of a polyphase matrix of a particular class of these oversampled filter banks. The lattice structure is based on the singular value decomposition for non-square matrices. The resulting lattice structure is able to provide fast implementation and allows us to determine the filter coefficients by solving an unconstrained optimization problem. The present filter banks can be regarded as generalizations of conventional lapped transforms. From this perspective, we call this filter bank the generalized lapped pseudo-biorthogonal transform (GLPBT). We show that the present systems with the lattice structure cover a wide range of linear-phase perfect reconstruction filter banks. We also show several design examples.