Design of 2-D quadrantally symmetric IIR digital filter using singular value decomposition and ordered real Schur form

A new technique is presented to design quadrantally symmetric 2-D IIR filters. This technique is based on two steps: first, the 2-D impulse response matrix (Hankel matrix) is decomposed by the SVD (singular value decomposition) to k parallel branches, each branch is composed of two cascaded single-input single-output (SISO) 1-D FIR filters. Second, a truncated model reduction algorithm is applied to the 1-D filters to approximate the N_l-dimensional FIR into n_l-dimensional IIR filters, where. n_l<N_l , l=1,2. The transformation that converts the FIR to IIR filters is obtained by finding the eigenspace associated with the large eigenvalues of the cross-gramian matrix W_co using the ordered real Schur form decomposition. Examples are given to illustrate the proposed technique