THEORY AND DESIGN OF 2-PARALLELOGRAM FILTER BANKS

It is well known that the analysis and synthesis filters of orthonorma l DFT filter banks can not have good frequency selectivity. The reason for this is that each of the analysis and synthesis filters have only one passband. Such frequency stacking (or configuration) in general d oes not allow alias cancelation when the individual biters have good s topband attenuation. A frequency stacking of this nature is called non permissible and should be avoided if good filters are desired. In a us ual M-channel filter bank with real-coefficient filters, the analysis and synthesis filters have two passbands. It can be shown that the con figuration is permissible in this case, Many designs proposed in the p ast demonstrate that filter banks with such configurations can have pe rfect reconstruction and good fitters at the same time, In this paper, we develop the two-parallelogram biter banks, which is the class of 2 -D filter banks in which the supports of the analysis and synthesis fi lters consist of two parallelograms. The two-parallelogram filter bank s are analyzed from a pictorial viewpoint by exploiting the concept of permissibility. Based on this analysis, we construct and design a spe cial type of two-parallelogram filter banks, namely, cosine-modulated filter banks (CMFB). In two-parallelogram CMFB, the analysis and synth esis filters are cosine-modulated versions of a prototype that has a p arallelogram support. Necessary and sufficient conditions for perfect reconstruction of two-parallelogram CMFB will be derived in the paper.