Analysis of realizable rational decimated nonuniform filter banks with direct structure

In the design of nonuniform filter banks (NUFBs) with direct structure, the location of each analysis filter, corresponding to the sampling factor satisfying maximal decimation condition, should be set properly to avoid large aliasing. In this paper, a necessary and sufficient condition for the setting of the location of each analysis filter is derived. The NUFBs, we focus on, have rational decimation factors. Based on the derived condition, the frequency support of each analysis filter for the realizable NUFBs can be determined directly in such a way that the analysis filters can extract the corresponding bands of the input signal. This provides a guideline for the design of NUFBs with direct structure in choosing proper locations of analysis filters.