TY - JOUR
T1 - A Unified Approach to the Optimal Synthesis of Fixed-Point State-Space Digital Filters
AU - Kawamata, Masayuki
AU - Higuchi, Tatsuo
PY - 1985/8
Y1 - 1985/8
N2 - This paper proposes two expressions of the output error variance due to coefficient quantization of fixed-point state-space digital niters in the time domain. One is the deterministic approach, which gives precisely the output error variance of state-space digital filters. The other is the statistical approach, where the errors of coefficient quantization are assumed to be independent random variables. The statistical approach gives a simple and easy way to analyze the output error variance due to coefficient quantization of state-space digitalfilters. The statistical coefficient sensitivity introduced by the statistical approach is shown to be equivalent to the roundoff noise power gain. Thus, state-space digital filters which are optimal with respect to both coefficient sensitivity arid roundoff noise can be synthesized by the method of minimization of the roundoff noise. Such optimal state-space digital filters which could be of any order are proved to be free of autonomous overflow limit cycles. A numerical example is given to illustrate the effectiveness of the analysis of the output error variance due to coefficient quantization and the synthesis method proposed here.
AB - This paper proposes two expressions of the output error variance due to coefficient quantization of fixed-point state-space digital niters in the time domain. One is the deterministic approach, which gives precisely the output error variance of state-space digital filters. The other is the statistical approach, where the errors of coefficient quantization are assumed to be independent random variables. The statistical approach gives a simple and easy way to analyze the output error variance due to coefficient quantization of state-space digitalfilters. The statistical coefficient sensitivity introduced by the statistical approach is shown to be equivalent to the roundoff noise power gain. Thus, state-space digital filters which are optimal with respect to both coefficient sensitivity arid roundoff noise can be synthesized by the method of minimization of the roundoff noise. Such optimal state-space digital filters which could be of any order are proved to be free of autonomous overflow limit cycles. A numerical example is given to illustrate the effectiveness of the analysis of the output error variance due to coefficient quantization and the synthesis method proposed here.
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U2 - 10.1109/TASSP.1985.1164638
DO - 10.1109/TASSP.1985.1164638
M3 - Article
AN - SCOPUS:0022270401
VL - 33
SP - 911
EP - 920
JO - IEEE Transactions on Acoustics, Speech, and Signal Processing
JF - IEEE Transactions on Acoustics, Speech, and Signal Processing
SN - 1053-587X
IS - 4
ER -