An algorithm for minimizing roundoff noise in cascade realizations of finite impulse response digital filters

Experimental results on roundoff noise in cascade realizations of Finite Impulse Response (FIR) digital filters are presented in this paper.∗ The entire roundoff noise distribution (i.e., over all possible orderings) is given for several low-order filters using both sum and peak scaling. Based on observations about this distribution, as well as intuitive arguments about the effects of ordering on roundoff noise, an algorithm for minimizing roundoff noise is presented. Experimental verification of this algorithm for a wide range of filters is given.