A Novel Method for Guaranteed Overflow Oscillation Elimination in Digital Filters Subject to Quantization

Abstract

This brief provides a novel criterion for the analysis of convergence of states of an infinite impulse response (IIR) digital filter to a bounded region under the influence of composite effects of quantization and overflow nonlinearities. The developed criterion is less conservative in its approach in terms of analyzing stability than conventional methods and can be employed for implementation of an IIR filter on comparatively smaller hardware word-length than existing methods. The conventional approaches consider asymptotic stability of a filter with respect to the quantization noise; however, quantization in digital filters can result into bounded oscillation and lead to infeasibility of the asymptotic stability. Therefore, a less conservative stability analysis together with estimation of steady-state region of convergence for an IIR filter is provided. In addition, the conventional approaches, analyzing stability, and steady-state region of convergence, may not guarantee an overflow oscillation-free realization of a filter. Consequently, a condition for estimating the steady-state region of convergence (along with the filter stability) with an additional constraint that the filter’s state should not overflow in the bounded region has been derived. A comparative analysis with conventional methods is provided in simulation results.