Minimizing the roundoff‐noise in digital filters by the branch and bound method
Hermann Lanfer, Ernst Lüder · International Journal of Circuit Theory and Applications · 1979
Abstract The branch and bound method is used for minimizing the roundoff‐noise in cascaded 2nd‐order filter sections. The degrees of freedom are the pole‐zero assignment and the ordering of the stages in the cascade, whereas the structure chosen is always the 2D‐form. During the search an upper and a lower limit for the noise power provide an estimate of how close the solution is to the optimum. Thus, the search may be stopped if no further substantial improvement can be expected. The optimum is reached when the two limits coincide. The efficiency of the procedure is demonstrated by optimizing three filters with up to 22nd‐order transfer functions.