Coefficient sensitivity and structure optimization of multidimensional state-space digital filters

In this paper, a new coefficient sensitivity measure for multidimensional (n-D) digital systems in state-space representation is proposed. This is motivated by the fact that coefficients equal to 0 or ±1 can be implemented exactly using finite wordlength and thus have no contribution to coefficient quantization errors. The relationship between commonly used sensitivity measures for 2-D and n-D systems and the new one proposed in this paper is discussed. It is shown that in evaluating the accuracy between a finite wordlength implementation of a transfer function and the ideal one, the proposed sensitivity measure is more useful than the commonly used ones. Further, the proposed measure confirms that realizations with Schur and/or Hessenberg structures can be used to obtain more accurate finite wordlength implementations of transfer functions than the ones obtained using fully parametrized minimum sensitivity structures