2-D diamond/quadrant FIR digital filter banks with sharp responses

This paper presents a novel design scheme, involving response sharpening process, for generating two-dimensional diamond/quadrant perfect-reconstruction (PR) linear-phase FIR filter banks with considerably reduced arithmetic operations, narrow transition bandwidth and good frequency selectivity. The scheme uses short 2-D Nyquist(M) subfilters, preferably multiplier-free ones, as basic building elements. Starting from a diamond/quadrant PR FIR filter bank based on the subfilters, the proposed scheme algebraically composes the building elements such that it refines the 2-D filter bank into a new 2-D filter bank with better frequency responses. The scheme can be successively applied till a satisfactory diamond/quadrant filter bank is obtained. The proposed scheme results in a tree-like multi-stage cascaded structure. It is composed of shared building elements with trivial coefficients and short wordlength lengths, which is suitable for finite-precision realization. The structure is highly modular, repetitive in all stages, and thus very suitable for VLSI implementation.