Realization of 2-D linear-phase FIR filters based on the singular-value decomposition

In this paper, the singular-value decomposition (SVD) technique is investigated for the realization of 2-D linear-phase FIR filters with arbitrary magnitude responses. A parallel realization structure consisting of a number of 1-D FIR filters is obtained by applying the SVD to the impulse response of a 2-D filter. By using the symmetry property of the 2-D impulse response and by developing an appropriate unitary transform, a singular-value decomposition with symmetric and skew-symmetric singular vectors is obtained so that the constituent 1-D filters have linear-phase characteristics. It is shown that the number of parallel sections can be reduced significantly by neglecting the smaller singular values without introducing a large error in the magnitude response of the simplified 2-D filter.