Design of shift-invariant nonuniform cosine-modulated filter bank with arbitrary integer sampling factors

Shift-invariance and unequal frequency partition are two desirable properties in many signal/image processing applications. In this paper, we treat a simple but efficient approach to design shift-invariant nonuniform cosine-modulated filter bank (SI-NCMFB) with arbitrary integer sampling factors. It consists of two subsystems where the first one is obtained by merging the consecutive subbands of a cosine-modulated filter bank, and the second one is derived under the condition of shift-invariance. By imposing the significant aliasing in the two subsystems to cancel each other structurally, the proposed SI-NCMFB achieves the properties of shift-invariance and flexible frequency partition. Since both the first and second subsystems come from just one prototype filter, the SI-NCMFB design is reduced to a filter design, leading to low design complexity. Furthermore, we extend the SI-NCMFB to two dimensions by separable operations. Unlike traditional separable transforms, the resulting 2D subbands have flexible directional-selectivity which is highly expected in image representation. Several simulation experiments are given to verify the proposed SI-NCMFB and the designed SI-NCMFB is of near-perfect reconstruction.