Statistical sensitivity and minimum sensitivity structures of 2-D separable-denominator digital filters

This paper proposes a statistical sensitivity of 2-D separabledenominator digital filters using the state-space approach. The sensitivity in this paper is represented by the controllability and the observability gramians and the state covariance matrix of the filters. The minimum sensitivity structures can be synthesized by giving an assumption to simplify the sensitivities. Numerical examples show that the proposed sensitivity is in very good agreement with the actual output error variance, and that minimum statistical sensitivity structures have a very small degradation of the frequency characteristic due to coefficient quantization.