An algorithm for constrained roundoff noise minimization in state-space digital filters

An iterative algorithm is presented for constructing an upper triangular matrix for use in transforming the coefficients in a state-space implementation of a recursive digital filter to reduce roundoff noise. Constraining the transformation matrix to be in this form provides a filter structure with a savings of N(N-1)/2 multiplies over the minimum noise realization with very little increase in roundoff noise gain. Background equations defining the roundoff noise reduction problem are given, the constrained noise minimization algorithm is derived, and a numerical example is presented to illustrate the effectiveness of the technique