Logarithmic Number System and Its Application in FIR Filter Design

Abstract

Data representation is an important parameter in the design of digital signal processors as it affects their performance and hardware complexity. Data representation influences the choice of algorithms and the hardware architecture, thus it has an impact on data storage requirements, processing performance, complexity, and power dissipation [1][2][3].The Logarithmic Number System (LNS) can be used to efficiently represent data in special-purpose processors. The efficiency of LNS stems from the properties of the logarithm exploited to reduce the basic arithmetic operations of multiplication, division, square roots, and squares to simple binary addition, subtraction, and right and left shifts, respectively [4]. Similarly, the computation of general roots and powers as well as of reciprocals are substantially simplified.Building on the reduced complexity of certain arithmetic operations, digital signal processor implementations can benefit from substantial architectural-level simplifications. Furthermore, beyond operation strength reduction, superior LNS dynamic range and numerical behavior, compared to conventional representations, are additional reasons that make LNS attractive. In order to fully utilize LNS potential, procedures are required to optimally define LNS design parameters and derive LNS solutions, matched to application specifications and requirements.