Analysis and optimal realization of pole-zero sensitivity for FIR digital filters

Abstract

Aiming at the deviation of pole and zero in filters which caused by the finite word length (FWL) effects,the sensitivity of pole and zero for FIR digital filters to coefficient errors was studied based on the state-space model.Unlike the IIR filter,the system matrix in state-space model of the FIR filter was defective.A set of generalized eigenvectors of defective matrix was introduced to analyze the pole sensitivity and derive the measure expression,and optimal realizations with respect to pole-zero sensitivity for FIR filters were proposed by finding optimal transformation matrices according to the similarity transformation theory.Theoretical analysis and simulation experiments show that the poles of a FIR filter are more sensitive to coefficient errors,and the proposed optimal realizations can reduce the sensitivity.

Keywords

• FIR digital filter;state-space realization;pole and zero sensitivity;defective matrix;generalized eigenvector