Noise reduction in 2-D separable-denominator digital filters using error feedback

This paper considers the problem of reducing the roundoff noise in two-dimensional separable-denominator digital filters using error feedback. Two error feedback paths are implemented with scaling factors in a two-dimensional separable-denominator digital filter implemented with a minimum number of delay elements. For each error feedback, the optimal solution of coefficients is obtained in a closed form to minimize the noise variance at the filter output. An illustrative example is given to demonstrate the validity of the proposed technique.