Design of Near-Perfect Reconstruction Two-Parallelogram Filter-Banks

Abstract—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 for-mulation of perfect-reconstruction (PR) cosine-modulated filter-banks (CMFBs) is proposed, with filters having a “two-parallel-ogram ” (Two-P) support. The design problem is considerably sim-plified 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 atten-uation. We achieve NPR by optimization of the polyphase compo-nents 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. Index Terms—Multidimensional filter banks, near-perfect re-construction (NPR), nonseparable filter banks, paraunitary. I