Roundoff noise characteristics of a class of orthogonal polynomial structures

The roundoff noise characteristics of three digital filter structures derived from the theory of orthogonal polynomials are studied and compared to the two standard forms, the direct and parallel forms. Both theoretical and experimental results are presented. It is shown that in terms of roundoff noise, the worst of the orthogonal filter forms (the two-multiplier lattice form) is superior to the direct form, and that the best (the normalized or ladder form) is nearly equal to or superior to the parallel form. The normalized form is shown to be vastly superior to the parallel form when filters with clustered poles are designed.