Theory, lattice structure and design of unequal length linear phase perfect reconstruction filter banks with more flexible length profile

This paper presents the structure and design of a class of linear phase perfect reconstruction FIR filter banks with unequal filter lengths. The motivation for design of such filter banks comes from image coding in order to simultaneously reduce the annoying blocking and ringing artifacts by long filters and short filters, respectively. First, the existence conditions are derived for such filter banks, which shows that the number of long filters can be arbitrary in some cases unlike earlier works which limit it to even number. Then, the proposed design methods structurally enforce the unequal length property along with linear phase and perfect reconstruction properties by lattice structures. Finally, several design examples are presented to confirm the validity of the approach and to compare the performance of different filter banks.