Roundoff noise in multirate digital filters (Q1059607)

Multistage multirate filters can be viewed as a cascade connection of single rate filters with rate changing switches between them. For such a model the calculation of the roundoff noise is difficult. In the paper new noise models (parallel connection) for multistage decimators and multistage interpolators are derived. These new models allow an easy calculation of the resulting roundoff noise. The new models are obtained through the application of the so-called commutative rule previously introduced by the same authors [ibid. 2, 361-386 (1983; Zbl 0526.93034); ibid. 3, 3-20 (1984; Zbl 0554.93045) and ibid. 3, 21-57 (1984; Zbl 0554.93046)]. For these schemes the noise variances and \(L_ p\) scalings are derived.