Flexible design of multidimensional perfect reconstruction FIR 2-band filters using transformations of variables

In this paper we present a method for designing multidimensional linear phase FIR diamond subband filters having the perfect reconstruction property. It is based on a transformation of variable technique and is equivalent to the generalized McClellan transformation. We present methods to design a whole class of transformations. The method provides the flexibility of controlling the frequency characteristics of the filters with ease. With this method the problem consists of two parts: design of the transformation and design of the 1-D filters. We first discuss the use of Lagrange halfband filters to design the I-D filters. We then present the modification of a particular Lagrange halfband filter which gives a pair of simple 1-D filters that are almost similar to each other in their frequency characteristics but still form a perfect reconstruction pair. The design technique is also extended to other types of 2-channel sampling lattice and subband shapes, in particular the parallelogram and the diagonally quadrant subband cases. Several numerical design examples are presented to illustrate the flexibility of the design method. An important feature of filters designed with this method is that efficient separable implementations are possible, even though the filters are nonseparable in the conventional sense.