Constrained minimization of roundoff noise in fixed-point digital filters

A method for the minimization of roundoff noise in fixed-point digital filters is presented. In this method, a given filter structure is transformed successively by small increments while roundoff noise is reduced at each step. For 1-D filter structures describable by a state-space model, the results obtained are similar to those of Mullis and Roberts (1) and Hwang (2). However, the new method has the important advantage that arbitrary portions of the topology of a structure can be held fixed while the structure is transformed. Thus, the number of new nonzero coefficients created by the transformation can be constrained. A simple example is presented showing a structure which has nearly as low roundoff noise as the "optimum" according to Mullis and Roberts (1) and Hwang (2), yet has much fewer non-zero coefficients than the latter.