A unified analysis of roundoff noise reduction in digital filters

Two seemingly unrelated roundoff noise reduction approaches, which lead to two distinct digital filter structures, i.e., the error-cancellation structure and the minimum roundoff-noise state-space structure, can be shown to share a common idea. This common idea is the following. The transfer function for the round-off errors is to be altered in such a way that the output noise is reduced in some sense, while the signal transfer function should remain intact. This idea is evident in the error-cancellation structure, however, it is disguised as the similarity transform in the state-space structure. This common idea can be formulated to relate the two approaches and form a new combined approach which seems to offer further insight and other low-noise structures.