Abstract
Logarithmic number system (LNS) is an attractive alternative to realize finite-length impulse response filters because of multiplication in the linear domain being only addition in the logarithmic domain. In the literature, linear coefficients are directly replaced by the logarithmic equivalent. In this paper, an approach to directly optimize the finite word length coefficients in the LNS domain is proposed. This branch and bound algorithm is implemented based on LNS integers and several different branching strategies are proposed and evaluated. Optimal coefficients in the minimax sense are obtained and compared with the traditional finite word length representation in the linear domain as well as using rounding. Results show that the proposed method naturally provides smaller approximation error compared to rounding. Furthermore, they provide insights into finite word length properties of FIR filters coefficients in the LNS domain and show that LNS FIR filters typically provide a better approximation error compared to a standard FIR filter.
Highlights
Finite-length impulse response (FIR) filters constitute a class of digital filters commonly used for their stability properties and the ability to obtain a linear phase response
As multiplications traditionally have a larger area complexity and power consumption compared to additions, much work has focused on reducing the number of multiplications in FIR filter realizations by using sparse filters or frequency response masking filters [3,4,5]
Important to note is that since the logarithmic number system (LNS) numbers will always be negative for FIR filter coefficients, there is no need to use a sign bit to represent the exponent in this case
Summary
Finite-length impulse response (FIR) filters constitute a class of digital filters commonly used for their stability properties and the ability to obtain a linear phase response. The main motivation for doing so is the inherent simplification of basic arithmetic operations as multiplication, division, roots, and powers, due to its properties, which are reduced to addition, subtraction, multiplications, and divisions, respectively They have interesting numerical properties as higher dynamic range compared to fixed-point representations for a given number of bits [13] and better round-off noise performance than floating-point arithmetic for a given number of bits [14,15,16]. An integer linear programming (ILP) approach to design optimal finite word length linear-phase FIR filters in the LNS domain is proposed. Important to note is that since the LNS numbers will always be negative for (most) FIR filter coefficients, there is no need to use a sign bit to represent the exponent in this case. In the LNS domain, the multiplier complexity is dependent on the smallest of the data and coefficient word lengths, while the adder complexity is dependent on the largest of those
Sign-in/Register to view highlights & summary 
Published Version (
Free)
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call