Design of near-perfect reconstruction two-parallelogram filter-banks

The design of nonseparable 2-D filter banks presents several difficulties, which do not arise in the 1-D counterparts. One particular aspect to be taken into consideration is the shape of the passbands of the filters. In the work of Lin and Vaidyanathan, a formulation of perfect-reconstruction (PR) cosine-modulated filter-banks (CMFBs) is proposed, with filters having a "two-parallelogram" (Two-P) support. The design problem is considerably simplified to the design of a single prototype-filter. In this letter, we extend the design method of Lin and Vaidyanathan to design near-perfect reconstruction (NPR) Two-P CMFBs, with the intention of trading off the PR property for filters with better stopband attenuation. We achieve NPR by optimization of the polyphase components of the prototype, imposing a "near power-complementary" constraint. We then demonstrate the better stopband attenuation achieved by the NPR design method, by comparing a PR and NPR design of a three-channel filter-bank