Synthesis of hybrid filter banks by global frequency domain least square solving

This paper introduces a simple method for designing hybrid filter banks (HFB) by solving a linear equation system directly derived from the perfect reconstruction conditions. The design starts with the knowledge of the analysis filters. FIR synthesis filters result after simple linear algebra computations so that the output of the HFB is as close as possible to a sampled and delayed version of the HFB input. In the case that only a smaller part of the input signal potential bandwidth is of interest, it is shown that the use of weighting functions stressing a certain frequency interval considerably improves the performance of the HFB.