Noise Reduction in Two-Dimensional Recursive Digital Filters with Discrete Optimized Error Feedback Coefficients

Abstract

This paper treats the minimization problem for roundoff noise in two-dimensional (2-D) recursive digital filters with an error feedback (EF). The EF is known as an available scheme for the reduction of roundoff noise, and this can be achieved by extracting a roundoff error from the quantizer and feeding it back to the adder. Since the EF circuit is an additional device of the digital filter, the bit length of the coefficients should be as short as possible for the fast arithmetic and low-cost realization. In this paper, we propose an algorithm to optimize the EF coefficients in a discrete space. The proposed algorithm is based on the branch and bound method by estimating the lower bound of the optimal solution, and the optimality of the obtained solution can be guaranteed. Finally, we give a numerical example to demonstrate the effectiveness of the proposed method, and show the optimal solution can be found without using the round-robin algorithm.