Finite wordlength design for IIR digital filters based on the modified least-square criterion in the frequency domain

The filter design problem is often formulated in real space (or complex space) whose word length is infinite. However, when implementing a filter in hardware, the frequency characteristic can be degraded caused by finite word-length effect. In this paper, we formulate the filter design problem based on modified least square criterion in the frequency domain. Here the problem is expressed as quadratic form and we optimize the filter coefficients by using branch and bound method in discrete space. In the branch and bound method, we calculate the relaxation solution based on the Lagrange multiplier method and search in the domain in which good possible solutions exist. In this method, the stable solutions whose poles are all inside the unit circle are just acceptable, so the stability of the filter can be guaranteed. Finally, numerical example is given to illustrate the utility of the proposed method.