New algorithms for the derivation of the transfer function matrix of two-dimensional digital filters

New algorithms for the derivation of the transfer function matrix of two-dimensional digital filters from their state-space representations are proposed. Two key steps in developing the new algorithms are reported. First, the transfer function is formulated in terms of the characteristic polynomials of the matrices involved. Second, an efficient algorithm for the identification of 1D polynomial coefficients is developed and is, in turn, used to determine the coefficient matrices of the 2D transfer function. As all the matrices of the 2D transfer function required in the first step can be obtained by inverting one complex matrix in conjunction with a few matrix multiplications and the second step leads to an unitary Vandermonde system, the proposed algorithms are computationally efficient and reliable. The efficiency of the algorithms is illustrated by an example