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1.	Alam, Syed Asad, 1984-, et al. (author) Design of Finite Word Length Linear-Phase FIR Filters inthe Logarithmic Number System Domain 2014 In: VLSI design (Print). - Egypt : Hindawi Publishing Corporation. - 1065-514X .- 1563-5171. ; 2014:217495 Journal article (peer-reviewed)abstract Logarithmic number system (LNS) is an attractive alternative to realize finite-length impulse response filters because ofmultiplication in the linear domain being only addition in the logarithmic domain. In the literature, linear coefficients are directlyreplaced by the logarithmic equivalent. In this paper, an approach to directly optimize the finite word length coefficients in theLNS domain is proposed. This branch and bound algorithm is implemented based on LNS integers and several different branchingstrategies are proposed and evaluated. Optimal coefficients in the minimax sense are obtained and compared with the traditionalfinite word length representation in the linear domain as well as using rounding. Results show that the proposed method naturallyprovides smaller approximation error compared to rounding. Furthermore, they provide insights into finite word length propertiesof FIR filters coefficients in the LNS domain and show that LNS FIR filters typically provide a better approximation error comparedto a standard FIR filter.

Alam, Syed Asad, 1984-, et al. (author)
Design of Finite Word Length Linear-Phase FIR Filters inthe Logarithmic Number System Domain
2014
In: VLSI design (Print). - Egypt : Hindawi Publishing Corporation. - 1065-514X .- 1563-5171. ; 2014:217495
Journal article (peer-reviewed)abstract
- Logarithmic number system (LNS) is an attractive alternative to realize finite-length impulse response filters because ofmultiplication in the linear domain being only addition in the logarithmic domain. In the literature, linear coefficients are directlyreplaced by the logarithmic equivalent. In this paper, an approach to directly optimize the finite word length coefficients in theLNS domain is proposed. This branch and bound algorithm is implemented based on LNS integers and several different branchingstrategies are proposed and evaluated. Optimal coefficients in the minimax sense are obtained and compared with the traditionalfinite word length representation in the linear domain as well as using rounding. Results show that the proposed method naturallyprovides smaller approximation error compared to rounding. Furthermore, they provide insights into finite word length propertiesof FIR filters coefficients in the LNS domain and show that LNS FIR filters typically provide a better approximation error comparedto a standard FIR filter.

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