A closed form solution to L/sub 2/-sensitivity minimization of second-order state-space digital filters

This paper proposes a closed form solution to L2-sensitivity minimization of second-order state-space digital filters. Restricting ourselves to the 2nd order case of state-space digital filters, we can formulate L2-sensitivity minimization problem by hyperbolic functions. As a result, L2-sensitivity minimization problem can be converted into a problem to find the solution to a 4th degree polynomial equation of constant coefficients, which can be algebraically solved in closed form without iterative calculations

[1]  Clifford T. Mullis,et al.  Synthesis of minimum roundoff noise fixed point digital filters , 1976 .

[2]  S. Hwang.  Minimum uncorrelated unit noise in state-space digital filtering , 1977 .

[3]  Allen G. Lindgren,et al.  Optimal synthesis of second-order state-space structures for digital filters , 1979 .

[4]  C. Barnes.  On the design of optimal state-space realizations of second-order digital filters , 1984 .

[5]  Masayuki Kawamata,et al.  A unified approach to the optimal synthesis of fixed-point state-space digital filters , 1985, IEEE Trans. Acoust. Speech Signal Process..

[6]  M. Kawamata,et al.  Statistical sensitivity and minimum sensitivity structures with fewer coefficients in discrete time linear systems , 1990 .

[7]  Wei-Yong Yan,et al.  On L/sup 2/-sensitivity minimization of linear state-space systems , 1992 .

[8]  Wei-Yong Yan,et al.  On L2-Sensitivity Minimization of Linear , 1992 .

[9]  M. B. Zarrop.  Book Review: Parametrizations in Control, Estimation and Filtering Problems , 1995 .

[10]  B. Moore,et al.  On L 2-Sensitivity Minimization of Linear State-Space Systems , 1996 .

[11]  Takao Hinamoto,et al.  A novel expression for L/sub 2/ sensitivity evaluation in state-space digital filters and its minimization , 1999, ISCAS'99. Proceedings of the 1999 IEEE International Symposium on Circuits and Systems VLSI (Cat. No.99CH36349).

[12]  Masayuki Kawamata,et al.  Design of Variable Digital Filters Based on State-Space Realizations , 2001 .

[13]  Takao Hinamoto,et al.  Analysis and minimization of L/sub 2/-sensitivity for linear systems and two-dimensional state-space filters using general controllability and observability Gramians , 2002 .