A well-conditioned quadratic program for unique design of two-dimensional weighted Chebyshev FIR filters

The weighted Chebyshev design of two-dimensional FIR filters is in general not unique since the Haar condition is not generally satisfied. However, for a design based on the discrete frequency domain, the Haar condition might be fulfilled. The question of uniqueness is, however, rather extensive to investigate. It is therefore desirable to define some simple additional constraints to the Chebyshev design in order to obtain a unique solution. The weighted Chebyshev solution of minimum Euclidean filter weight norm is always unique, and represents a sensible additional constraint since it implies minimum white noise amplification. It is shown that this unique Chebyshev solution can always be obtained by using an efficient quadratic programming formulation with a strictly convex objective function and linear constraints. An example where a conventional Chebyshev solution is non-unique is discussed.