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 orthor hombic) lattice. The ideal 3-D sub-band is of the truncated octahedron shape. The design technique is based transformation of variable metho d equivalent to the generalised McClellan transformation, The filters are FIR, have linear phase and achieve perfect reconstruction. Althoug h the sub-band shape is quite complicated, the ideal frequency charact eristics are well approximated, This is illustrated with an example, T he technique provides the flexibility of controlling the frequency cha racteristics of the filters with ease. The filters can be implemented quite efficiently due to the highly symmetrical nature of the coeffici ents of the transformation. The authors also modify and extend the bas ic design technique to impose the zero property (the number of zeros o f the filter transfer function at the aliasing frequency) on the sub-b and filters, This property is important when the filter bank is used i teratively in a tree-structured manner as a discrete wavelet transform system and the issue of regularity arises, Several design examples ar e presented to illustrate the design technique.