A direct method for minimizing the roundoff noise in digital filter design

The authors consider the problem of reducing the effects of roundoff noise and coefficient sensitivity in digital filters when implemented with fixed point arithmetic. The minimum roundoff noise and minimum sensitivity structures have generally many more coefficients than the other canonical structures. A direct method is provided for constructing a reduced sensitivity and roundoff noise state space realization of a digital filter with a saving of 1/2n(n-1) multiplies over the optimal structures. The method avoids expensive transformation of the original realization to the balanced form as well as iterative algorithms of constrained and unconstrained noise minimization. A systolic array implementation is also presented