Design for 2-D error feedback networks with identical coefficient sets

In realization of recursive digital filters with fixed point arithmetic, an error caused by roundoff arises. It is known that the level of the roundoff noise of an IIR filter tends to be high when the poles are close to the unit circle. Error feedback (EF) is an effective method to reduce the roundoff noise. It is desirable to design an EF network using as few parameters as possible in order to keep computational costs low. In this paper, we propose a method for designing a 2D EF network with identical coefficient sets. That is, the EF coefficients are divided into several subsets such that all the elements within each set have the same absolute value. In order to optimize the coefficient sets, we propose an algorithm by using the genetic algorithm. In the numerical example, we demonstrate the effectiveness of the proposed method.