Design of two-dimensional recursive digital filters based on the optimal decomposition of magnitude specifications

The authors present a novel decomposition technique called the optimal decomposition (OD) for decomposing 2-D magnitude specifications into 1-D ones. By using the OD, 2-D magnitude specifications can be decomposed into 1-D ones which are always nonnegative, and the root mean square (rms) decomposition error is minimum. As a result, the problem of designing a 2-D digital filter can be reduced to one of designing a pair of 1-D digital filters. Thus, the original 2-D design problem can be significantly simplified. A numerical example is given to illustrate the OD-based design technique.