Novel characteristics of even-stacked cosine-modulated filter banks: Non-redundant directional transform and shift-invariance

In this paper, we present non-redundant directional transform and shift-invariant transform based on even-stacked cosine-modulated filter banks (ECFBs). M-band dual-tree wavelet transform (MDTWT) recently proposed has rich directional selectivity and near shift-invariance. However, it has two problems. First, it is not critically-sampled transform. Second, it cannot achieve shift-invariance at all decomposition levels. For these problems, we show a solution based on ECFBs. Critically-sampled ECFBs provide non-redundant transform with rich directional selectivity. Furthermore, oversampled ECFBs with oversampling ratio of 2 can assure the shift-invariance at any decomposition levels. Moreover, ECFBs can be designed from only one prototype filter and guarantee linear phase. In this paper, we verify these facts by theoretical analysis and simulations.