An algorithm for optimally ordering the sections of a cascade digital filter

An efficient algorithm is presented for ordering the sections of a cascade structure digital filter in such a way as to minimize the output noise power due to internal multiplier roundoff error. The algorithm is applicable to either recursive or non-recursive filters, and is not limited to a particular section form or method of intersection scaling. Computation time estimates are given for recursive filters as a function of order. Implications of the technique relative to the theory of dynamic programming are discussed.