Noise reduction in state-space digital filters using high-order error feedback

This paper treats noise reduction in state-space digital filters using high-order error feedback. A technique is developed for obtaining the optimal error feedback coefficients that minimize the variance at the filter output. This is done by minimizing a quadratic form subject to the coefficients of the error feedback being symmetric or antisymmetric. The optimal solution can be characterized in a closed form by applying the Lagrange multiplier method. In an unconstrained case, the optimal error feedback corresponds to a special case of the above optimal solution. Finally, a numerical example is given to illustrate the utility of the proposed technique.