An efficient technique for the design of 2-D recursive digital filters with guaranteed stability

A technique is developed for designing two-dimensional (2-D) recursive digital filters with guaranteed stability. The filter is described by a 2-D rational transfer function which corresponds to a linear difference equation with either rectangular or triangular input and output masks. In the case of rectangular (triangular) input and output masks, the denominator polynomial is derived from the stable matrix of the Roesser model (the Fornasini-Marchesini second model). In the proposed technique, the denominator and numerator of the filter are designed separately and recursively. First, the denominator coefficients are found by minimizing a performance index through the alternating variable method. The numerator coefficients are then determined analytically by solving linear simultaneous equations. The above process will be repeated until there is negligible change in the objective function. Finally, a numerical example is given to illustrate the utility of the proposed technique.