Admissibility of unstable second-order digital filters with two's complement arithmetic

摘要

In this paper, we have extended the existing results on the admissible set of periodic symbolic sequences of a second-order digital filter with marginally stable system matrix to the unstable case. Based on this result, the initial conditions can be computed using the symbolic sequences. The truncation error of the representation of an initial condition due to the use of a finite number of symbols is studied.