"In this paper, a novel approach is proposed
to analyze and minimize fixed-point arithmetic errors for
digital filter implementations based on eigenvalue sensitivity
measures. First, uncertainties of the filter-parameter caused by
roundoff and computational errors are expressed in function
of register length for fixed-point implementations. Sequentially, based on fixed-point statistical model and normal-form
transformation, a stability criterion of the dynamical filter
model is derived to form a similarity transformation with
a sufficient and necessary condition of the stability. Thus,
eigenvalue sensitivity measure with respect to filter parameters
is constructed in the sense of induced 2-norm. This measure is
minimized by an optimal similarity transformation (normalform transformation) obtained from an analytically algebraic
method. Based upon this transformation as well as the stability
criterion, a least register length can be obtained. Finally, an
example is performed to illustrate the effectiveness of the
proposed scheme."
