Floating-point roundoff noises of first- and second-order sections in parallel form digital filters

Assuming wide-sense stationary white noise input, we investigated the floating-point roundoff noises of first- and second order digital subfilters. For first-order subfilters, the roundoff noise of parallel form 3P realization is invariably smaller than that of the corresponding parallel form 1P realization. The floating-point roundoff noise of a second-order subfilter depends on the order of additions. Criteria are developed to find the best order and to make the choice between parallel form 1P and 3P realizations.