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A new approach to the realization of two-dimensional (2- D) FIR and IIR digital filters is introduced based on the so-called "lower-upper triangular (LU) decomposition" of matrix coefficients of their two-dimensional polynomials. It is demonstrated that the LU realization scheme enjoys a number of attributes for VLSI implementation including high parallelism, modularity, and regularity. This paper also shows that the computational requirements of the LU realization structure are much smaller than those of the Jordan (JD), singular value (SV), and canonical (direct) realizations. Furthermore, it is shown that if a canonical 2-D IIR filter is realizable, then a realizable LU decomposition form can be always obtained, a property that is not shared by the JD and SV decomposition forms. Finally, the extension of the LU decomposition approach to the realization of m-D digital filters is discussed.