The logarithmic number system for strength reduction in adaptive filtering
John R. Sacha, M.J. Irwin · 1998
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.