Normal realizations of IIR digital filters

Normal realizations of IIR digital filters possess many desirable properties including freedom from overflow oscillations, low coefficient sensitivity, and invariance of form and roundoff noise under frequency transformations of the filter. Normal realizations are closely related to minimal roundoff noise structures. Given a state variable model {A,b,c,d} of a filter, we define a normal structure as a filter whose A matrix satisfies AA^T=A^TA. This paper develops design equations and roundoff noise equations for normal and minimal roundoff noise filters in terms of the poles and zeros of the filter transfer function. The development has geometric interpretations which yield additional insights into low roundoff noise structures.