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The design problem of two-dimensional digital filters is the subject of this paper. The problem is formulated for both FIR and IIR filters in such a way that the performance index is a convex function of the optimization vector. The design technique is based on Newton's method. Each iteration consists of N easily computed steps, where N is the number of parameters to be optimized. The coefficients can be obtained in the quantization levels according to the desired number representation, Illustrative examples and comparisons with existing techniques are also included.