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

This paper studies the roundoff noise and the scaling in 2-D state space digital filters. The noise matrix and the covariance matirx in the 2-D case are derived. They are expressed with infinite sum or double integral. A formulation is given to synthesize minimum roundoff noise 2-D state space digital filters. A numerical example is given to show the methods of analysis and synthesis.