Perfect Reconstruction Nonuniform Filter Banks with Linear Phase

A nonuniform filter bank divides the band nonuniformly according to the properties of the signal, which is expected to be more effective than a uniform division filter bank in applications such as subband coding. The structure of the nonuniform filter bank, however, is complex. In particular, no investigation has been made of the linear-phase nonuniform filter bank. From such a viewpoint, this paper considers a perfect reconstruction nonuniform filter bank with linear phase, and derives the necessary and sufficient conditions for a perfect reconstruction system as well as for a linear-phase filter. Then, a design method is presented based on the amplitude distortion in the frequency domain and the elimination of aliasing. By the proposed method, the nonuniform filter bank can be designed directly without using the equivalent transformation to the uniform filter bank.