Finite wordlength implementation for recursive digital filters with error feedback

In this work, we treat a design problem for recursive digital filters described by rational transfer function in discrete space with scaling and error feedback. First, we form the filter design problem using the least-squares criterion and express it as the quadratic form with respect to the filter coefficients. Next, we show the relaxation method using the Lagrange multiplier method in order to search for the good solution. Finally, we show the effectiveness of the proposed method using some numerical examples.