A unified study on the roundoff noise in 2-D state space digital filters

Abstract

This paper studies the roundoff noise and the scaling in 2-D state space digital filters. The noise matrix and the covariance matrix in the 2-D case are derived. They are expressed with double infinite sums or double integral. A formulation is presented to synthesize minimum roundoff noise 2-D state space digital filters. A practical synthesis procedure is also provided. A numerical example is given to show the analysis method and synthesis method presented here.