On the Arbitrary-Length $M$-Channel Linear Phase Perfect Reconstruction Filter Banks
Zhiming Xu, Anamitra Makur · IEEE Transactions on Signal Processing · 2009
This correspondence extends the theory and lattice factorizations forM-channel linear phase perfect reconstruction filter banks (LPPRFBs). We deal with FIR FBs with real-valued filter coefficients in which all filters have the samearbitrarylength L = KM + beta (0 les betaL=KM. First, refined existence conditions on this larger class of FBs are given. Then, lattice structures are developed forbothodd 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 beminimalin terms of the number of delay elements used in implementation, and tocompletelyspan the class of LPPRFBs with lengthLles 2Mand the whole class of linear phase paraunitary filter banks (LPPUFBs).