Design of two-dimensional recursive digital filters

The present paper develops a design technique for approximating nonseparable frequency characteristics by sums and products of separable transfer functions. This approximation is called the "piecewise separable" decomposition of the characteristic. In the design technique, the desired filter with half-plane symmetry (radial symmetry) is obtained by shifting a low-pass characteristic in the frequency domain, and by combining these shifted characteristics. Also the paper includes design approaches for the four-quadrant symmetry filters. Two examples illustrate the technique of the paper.