On the Interaction of Roundoff Noise and Dynamic Range in Digital Filters

The interaction between the roundoff‐noise output from a digital filter and the associated dynamic‐range limitations is investigated for the case of uncorrelated rounding errors from sample to sample and from one error source to another. The required dynamic‐range constraints are derived in terms of Lp norms of the input‐signal spectrum and the transfer responses to selected nodes within the filter. The concept of “transpose configurations” is introduced and is found to be quite useful in digital‐filter synthesis; for although such configurations have identical transfer functions, their round‐off‐noise outputs and dynamic‐range limitations can be quite different, in general. Two transpose configurations for the direct form of a digital filter are used to illustrate these results. © 1970 The Bell System Technical Journa