The logarithmic number system for strength reduction in adaptive filtering

  • Authors:
  • John R. Sacha;Mary Jane Irwin

  • Affiliations:
  • Computer Science and Engineering Department, The Pennsylvania State University, University Park, PA;Computer Science and Engineering Department, The Pennsylvania State University, University Park, PA

  • Venue:
  • ISLPED '98 Proceedings of the 1998 international symposium on Low power electronics and design
  • Year:
  • 1998

Quantified Score

Hi-index 0.00

Visualization

Abstract

An important technique for reducing pow er consumption in VLSI systems is strength reduction, the substitution of a less-costly operation such as a shift, for a more-costly operation such a multiplication. Using a logarithmic number represen tation provides sev eral opportunities for strength reductions; in particular, m ultiplicationis performed as the fixed-point addition of logarithms, and extracting a square root is implemented via a shift. These reductions occur transparently at the hardware level; consequently relativ ely little algorithmic modification is required, and they are readily applicable to adaptive filtering. For performing Givens rotations in the QR decomposition recursiv e least squares adaptive filter, logarithmic arithmetic is shown to compare favorably to other strength reduction techniques, such as CORDIC arithmetic, in terms of switched capacitance and numerical accuracy.