An efficient state-space realization with minimum roundoff noise gain

作者：Zhao Zixue^*

来源：IEEE Transactions on Circuits and Systems I-Regular Papers, 2007, 54(2): 432-440.

DOI：10.1109/TCSI.2006.885696

• direct-form II transposed (DFIIt) structure
• error feedback
• polynomial parametrization
• rounding before multiplication (RBM)
• roundoff noise
• state-space realization

This paper deals with efficient digital filter structures with roundoff noise consideration. Motivated by the direct-form II transposed (DFIIt) structure in rho-operator (rho DFIIt) an alternative structure is obtained [Li et al. in 2005, where, instead of the first-order rho-operators in rho DFIIt, a set of second-order polynomial operators is used. In this paper, with the rounding before multiplication implementation taken into account, the equivalent state-space realization of the proposed structure by Li et al. is derived and its roundoff noise performance is analyzed by deriving the roundoff noise expressions without/with error feedback consideration. This state-space realization can be efficiently implemented and has more degrees of freedom than its counterpart rho DFIIt, which can be utilized to-minimize the roundoff noise gain. A genetic algorithm is proposed to efficiently solve the optimal structure problem. Extensive examples are given to illustrate the advantage of this state-space realization and support the theoretical analysis.

• 出版日期2007-2
• 单位南阳理工学院