Logarithmic number system (LNS) is an attractive alternative to realize finite-length impulse response filters because of\nmultiplication in the linear domain being only addition in the logarithmic domain. In the literature, linear coefficients are directly\nreplaced by the logarithmic equivalent. In this paper, an approach to directly optimize the finite word length coefficients in the\nLNS domain is proposed. This branch and bound algorithm is implemented based on LNS integers and several different branching\nstrategies are proposed and evaluated. Optimal coefficients in the minimax sense are obtained and compared with the traditional\nfinite word length representation in the linear domain as well as using rounding. Results show that the proposed method naturally\nprovides smaller approximation error compared to rounding. Furthermore, they provide insights into finite word length properties\nof FIR filters coefficients in the LNS domain and show that LNS FIR filters typically provide a better approximation error compared\nto a standard FIR filter.
Loading....