A transformation method for the design of two-dimensional circularly-symmetric FIR digital filters

A new transformation method for the design of 2-D FIR digital filters with circular band boundaries is proposed. The method involves a simple transformation on an optimal 1-D FIR prototype filter design which is followed by a 2-D windowing operation. The method results in designs with excellent band-boundary circularity, even for high-frequency band boundaries. As shown by the examples, the approximation errors in the passband and stopband are nearly optimal and are typically within 10% of the optimal L_∞ solution. Since the designs are nearly optimal, it is expected that the method may also be useful for generating an initial estimate for optimization methods. An additional result of this work is a technique for estimating the required order of 2-D FIR digital filters that meet prescribed specifications