Design of oversampled nonuniform filter banks with arbitrary rational frequency partitioning

Among the theory and design of oversampled nonuniform filter banks (NUFBs), most of the existing works only consider the cases with integer decimators, and up to now the issue with rational sampling factors has not been discussed yet. In this paper, we generalize the partial modulation technique to realize arbitrary rational frequency partitioning of oversampled NUFBs with highly desired linear-phase (LP) property. Further for the subbands with sampling factors violating the guard band restriction, a phase-modification scheme is derived to avoid uneliminable large aliasing and meanwhile preserving the LP characteristics of shifted analysis/synthesis filters. By using the proposed method, the design issue of LP oversampled NUFBs can be reduced to that of several prototypes, decreasing the design complexity largely. As illustrated by examples, the proposed algorithm is more general in terms of arbitrary rational decimation and thus has broad application prospects.