Design of perfect reconstruction finite impulse response (FIR) 2-channel filter banks in 3D with face-centered orthorhombic (FCO) sampling using transformations of variables

In this paper we present a technique to design 2-channel filter banks in 3 dimensions where the sampling is on the FCO (face centered orthorhombic) lattice. The ideal 3-D subband is of the truncated octahedron shape. It is based on the transformation of variable method and it is equivalent to the generalized McClellan transformation. The filters are FIR, have linear phase, and achieve perfect reconstruction. Although the subband 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.