Toward Local Stability Analysis of Externally Interfered Digital Filters Under Overflow Nonlinearity

Abstract

This brief focuses on the local stability analysis of 1-D digital filters that are subject to the saturation overflow nonlinearity and external interference by exploiting local saturation arithmetic. A novel stability criterion that analyzes the local asymptotic stability of a digital filter under zero external interference is investigated. Furthermore, an extension to attain a local ${H}_{\infty}$ performance is developed to tackle the external interference. The conventional global stability criteria using the global saturation arithmetic can be derived as specific cases of the proposed local results. The proposed local stability criteria provide a lesser conservative estimate of interference attenuation level in comparison with existing global techniques. Furthermore, information on the tolerable energy bound on external interference for a given attenuation level is also revealed contrary to global schemes. In addition to this, the proposed methodology can be applied to evaluate the minimum word length to achieve the desired fixed-point resolution and the performance specifications for the sake of hardware optimization. A novel two-step approach is also provided for solving the filter stability analysis condition using convex routines. A numerical example is presented to demonstrate these features.