MINIMUM NORM DESIGN OF 2-DIMENSIONAL WEIGHTED CHEBYSHEV FIR FILTERS

The weighted Chebyshev design of two-dimensional FIR filters is in gen eral not unique since the Haar condition is not generally satisfied. H owever, for a design on a discrete frequency domain, the Haar conditio n might be fulfilled. The question of uniqueness is, however, rather e xtensive to investigate. It is therefore desirable to define some simp le 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 additi onal constraint since it implies minimum white noise amplification. Th is unique Chebyshev solution can always be obtained by using an effici ent quadratic programming formulation with a strictly convex objective function and linear constraints. An example where a conventional Cheb yshev solution is nonunique is discussed in the brief.