Tree-structured IIR/FIR uniform-band and octave-band filter banks with very low-complexity analysis or synthesis filters

This paper introduces new tree-structured uniform-band and octave-band digital filter banks (FBs). These FBs make use of half-band IIR filters in the analysis FBs and FIR filters in the synthesis FBs. The resulting FBs are asymmetric in the sense that the analysis FB has a very low arithmetic complexity whereas that in the synthesis FB is higher. However, compared with other asymmetric FBs, the proposed ones have in many cases a lower overall arithmetic complexity and delay. The proposed FBs have magnitude distortion but no phase distortion; further, the aliasing components are either zero (uniform-band case) or approximately zero (octave-band case). The FBs are designed using linear and nonlinear programming. Design examples are included demonstrating the properties of the proposed filters banks.