TY - JOUR

T1 - A Unified Approach to the Optimal Synthesis of Fixed-Point State-Space Digital Filters

AU - Kawamata, Masayuki

AU - Higuchi, Tatsuo

N1 - Copyright:
Copyright 2015 Elsevier B.V., All rights reserved.

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.

UR - http://www.scopus.com/inward/record.url?scp=0022270401&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0022270401&partnerID=8YFLogxK

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 -