A New Method for the Design of Two-Dimensional Recursive Digital Filters

A new method for designing general two-dimensional digital recursive filters is presented. This method involves an iterative optimization procedure which is based on a modified Marquardt algorithm. The error function to be minimized is composed of the real part and imaginary part of frequency response error, and stability error which is computed in the spatial domain. Analytic formulas for the derivatives of error function with respect to filter coefficients are derived. Therefore, the error derivatives required in the optimization procedure can be calculated analytically rather than numerically. This results in saving design time significantly. We present several examples to demonstrate the design capability and the efficiency of this method.