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An Efficient State-Space Realization With Minimum Roundoff Noise Gain

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1 Author(s)
Zixue Zhao ; Sch. of Electr. & Electron. Eng., Nanyang Technol. Univ., Singapore

This paper deals with efficient digital filter structures with roundoff noise consideration. Motivated by the direct-form II transposed (DFIIt) structure in rho-operator (rhoDFIIt) an alternative structure is obtained [Li in 2005, where, instead of the first-order rho-operators in rhoDFIIt, 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 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 rhoDFIIt, 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

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Circuits and Systems I: Regular Papers, IEEE Transactions on  (Volume:54 ,  Issue: 2 )