The use of strictly causal filters in the approximation of two-dimensional asymmetric half-plane filters

This paper considers the problem of approximating twodimensional (2-D) asymmetric half-plane digital filters using strictly causal filters. A technique is developed by means of certain mapping techniques and singular value decomposition of two finite Hankel matrices. First, a given impulse response over an asymmetric half-plane is transferred into the open first quadrant via an invertible mapping. Second, the data in the transformed domain (open first-quadrant) are approximated by a strictly causal separable-denominator recursive filter using singular value decomposition. Finally, the resultant filter is transferred back to the original coordinates. Since the resulting filter is simpler than a causal filter being separable in the denominator, the implementation is advantageous in addition to having a very easy stability check. Two examples are presented to illustrate the utility of the proposed technique.