Design of nonseparable 3-D filter banks/wavelet bases using transformations of variables

The authors present a technique to design two-channel filter banks in three dimensions where the sampling is on the FCO (face centred orthorhombic) lattice, The ideal 3-D sub-band is of the truncated octahedron shape. The design technique is based transformation of variable method equivalent to the generalised McClellan transformation. The filters are FIR, have linear phase and achieve perfect reconstruction. Although the sub-band shape is quite complicated, the ideal frequency characteristics are well approximated. This is illustrated with an example. The technique provides the flexibility of controlling the frequency characteristics of the filters with ease. The filters can be implemented quite efficiently due to the highly symmetrical nature of the coefficients of the transformation. The authors also modify and extend the basic design technique to impose the zero property (the number of zeros of the filter transfer function at the aliasing frequency) on the sub-band filters. This property is important when the filter bank is used iteratively in a tree-structured manner as a discrete wavelet transform system and the issue of regularity arises. Several design examples are presented to illustrate the design technique