Design of 2-D separable-denominator digital filters based on the reduced-dimensional decomposition

The paper proposes a technique for the design of 2-D separable-denominator digital filters. The technique is based on decomposing both 2-D separable-denominator state-space models and the given 2-D impulse response specifications into 1-D ones. It is proved that the given 2-D specifications can be optimally decomposed into 1-D specifications via singular value decompositions. Then, 1-D digital filters are designed to approximate the decomposed 1-D specifications. By using balanced approximation as the 1-D design algorithm, a practical algorithm is presented to design stable 2-D separable-denominator digital filters. The algorithm is computationally efficient and numerically stable.