Realization of two-dimensional digital filters by LU decomposition of their transfer function

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 shown that a general two-dimensional transfer function can be exactly realized in terms of polynomials of order one, each one of which is a function of one of the two space variables only. It is demonstrated that the LU realization scheme exhibits high inherent parallelism as well as great modularity, regularity and flexibility. This paper also shows that the computational requirements of the LU realization are much less than these of the Jordan (J), Singular Value (SV) and canonical realization schemes.