A Measure of Coefficient Quantization Errors for Linear Discrete-Time State-Space Systems

Shumon SAITO  Masayuki KAWAMATA  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E84-A   No.8   pp.1815-1821
Publication Date: 2001/08/01
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Digital Signal Processing)
Category: Digital Filter
linear discrete-time systems,  state-space systems,  coefficient sensitivity,  wordlength effects,  

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This paper proposes a measure of coefficient quantization errors for linear discrete-time state-space systems. The proposed measure of state-space systems agrees with the actual output error variance since it is derived from the exact evaluation of the output error variance due to coefficient deviation. The measure in this paper is represented by the controllability and the observability gramians and the state covariance matrix of the system. When the variance of coefficient variations is very small, the proposed measure is identical to the conventional statistical sensitivity of state-space systems. This paper also proposes a method of synthesizing minimum measure structures. Numerical examples show that the proposed measure is in very good agreement with the actual output error variance, and that minimum measure structures have a very small degradation of the frequency characteristic due to coefficient quantization.