Noise reduction for 3-D IIR digital filters with discrete error feedback coefficients

In this paper, we propose a new design method for error feedback (EF) with discrete coefficients in order to reduce the roundoff noise in 3-D IIR digital filters. The lower bound estimation principle is used so that finding the optimum solution. Using the proposed method, the EF designed by the proposed method has guaranteed optimality. Additionally, the method can reduce the calculation cost because we can terminate lots of branches based on the lower bound estimation principle. Finally, we present a numerical example by designing the (2, 2, 2)th order EF with discrete coefficients whose word-length is 7 bits. Also, we compare the proposed method with the simulated annealing and simple rounding. From the results, we demonstrate the effectiveness of the proposed method.