On the Arbitrary-Length $M$ -Channel Linear Phase Perfect Reconstruction Filter Banks

This correspondence extends the theory and lattice factorizations for M-channel linear phase perfect reconstruction filter banks (LPPRFBs). We deal with FIR FBs with real-valued filter coefficients in which all filters have the same arbitrary length L = KM + beta (0 les beta < M) and same symmetry center, in contrast to traditional constrained length profile L=KM. First, refined existence conditions on this larger class of FBs are given. Then, lattice structures are developed for both odd and even-channel FBs, and their relationship with time-domain lapped transforms is explained. These structures are more general compared to conventional design methods, and cover them as special cases. Furthermore, we discuss how to structurally impose the regularity onto the lattice structure to ensure the smoothness of the basis function, which is very desirable in high performance image compression. Finally, these lattice structures are proven to be minimal in terms of the number of delay elements used in implementation, and to completely span the class of LPPRFBs with length L les 2M and the whole class of linear phase paraunitary filter banks (LPPUFBs).