Nested transformation of variables for designing multidimensional filter banks

The transformation of variables has been shown previously to be a flexible technique for designing multidimensional multirate filter banks. The flexibility is due to the relative ease in designing the transformation function to shape the characteristics of the resulting subband filters. A new approach is presented where a nested transformation is used. The design of 2-D quincunx lattice and 3-D face centered orthorhombic (FCO) lattice filter banks is considered. Causal and stable IIR subband filters are possible and the impulse response supports are in the first-quadrant and first-octant for the 2-D and 3-D cases respectively.