Synthesis of two-dimensional IIR digital filters with desired spatial domain specifications and no overflow oscillations

Abstract

A design technique of two-dimensional (2D) recursive infinite-area impulse response (IIR) digital filters (DFs) which approximates desired spatial-domain specifications and guarantees no overflow oscillations is proposed in this paper. First, it is shown that the balanced approximation is not optimal for l2 model reduction. From this point of view, a new design technique of 2D separable-denominator (SD) digital filters is studied using reduced-dimensional decomposition and the l2 model reduction methods based on balanced gains. This result is used as a starting point of a design algorithm for 2D non-separable ND DFs. Second, a design problem of 2D ND DFs is formulated as a nonlinear minimization problem with equality and inequality constraints, and the Broyden-Fletcher-Goldfarb-Shanno algorithm is applied to solve it. Finally, two examples are given to show the effectiveness of the proposed design technique.