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The present paper presents a new technique for the design of multidimensional FIR digital filters. Given the desired amplitude respinse, the truncation error, of a low-order approximation to a high-order filer" is iteratively decreased by varying the phase response. Convergence of the iterative algorithm is discussed. Examples illustrating the use of the technique are included. The design method is formulated for twodimensional filters, however filters of any dimension may be designed by this technique.