Design of unequal-length linear-phase filter banks without redundancy

In this paper, we present a new structure for linear-phase filter banks without redundancy, which have unequal-length filters at each sub-band. First, we extend the simplified lattice structure of the linear-phase filter bank to the unequal-length linear-phase paraunitary filter bank. In general, the unequal-length linear-phase paraunitary filter bank has equal-length filters at both the analysis and the synthesis bank because the synthesis bank is a transposed version of the analysis one, while the biorthogonal one does not. So, we discuss the conditions that the linear-phase biorthogonal filter bank has unequal-length filters at 1) the analysis bank, 2) the synthesis bank, and 3) both the analysis and the synthesis banks. Finally, several design and image coding examples are shown.