A design procedure for oversampled nonuniform filter banks with perfect-reconstruction

We describe a time-domain procedure for designing the synthesis filters of perfect-reconstruction oversampled filter banks. A condition matrix is derived from the basic magnitude distortion and aliasing canceling conditions and we derive the necessary and sufficient conditions for perfect reconstruction. The formulation is general for any decimation scenario, but it is particularly useful with nonuniform decimation. Further, the condition matrix in the proposed design model is in general rectangular and has a nonzero null-space which allows for design optimization.