Optimal realization of multidimensional digital filters

The optimal synthesis of a SISO multidimensional (M-D) digital filter with fixed-point arithmetic is investigated. A general upper bound on the sensitivity measurement of the filter´s eigenfunctions is proposed. It is shown that for optimal realization this bound attains its minimum value. It is found that the optimal realizations of M-D filters demonstrate a remarkable property in needed number of multipliers per sample output. A numerical example is presented to illustrate the design procedure.