Maximally flat nonrecursive two-dimensional digital filters

The maximally flat criterion is extended to the design of two-dimensional nonrecursive digital filters which approximate circularly symmetrical low-pass specifications. Straightforward generalization of the one-dimensional method does not completely specify the coefficient matrix of the filter. The additional degrees of freedom can be used to increase locally the order of flatness at the origin and/or at the Nyquist frequencies. The choice of the local conditions is crucial, in particular for what regards the monotonic behavior outside the axes. Concentration of the local conditions on the diagonal of the frequency plane gives a special class of filters which, besides the advantage of closed-form expressions for the coefficients, has a monotonically decreasing frequency response along any radius of the frequency plane.