Least pth power design and characterization of affine phase complex 2-D filters and the min-max approximation

Affine phase 2-D filters are designed using the p^th power norm to measure its deviation from an idealized affine phase filter response not necessarily symmetric. Necessary and sufficient conditions are derived in terms of its coefficients for the filter to be affine phase. The 2-D design is obtained in closed form for p=2. Next the design is generalized for 2<p where the solution is not obtainable in closed form but by the use of the complex Newton method iteration. Convergence is attained after a modest number of iterations by making p increase by a constant factor at each iteration. For large p solution approaches the min-max. Several examples are provided