Word-length optimization for differentiable nonlinear systems

Abstract

This article introduces an automatic design procedure for determining the sensitivity of outputs in a digital signal processing design to small errors introduced by rounding or truncation of internal variables. The proposed approach can be applied to both linear and nonlinear designs. By analyzing the resulting sensitivity values, the proposed procedure is able to determine an appropriate distinct word-length for each internal variable in a fixed-point hardware implementation. In addition, the power-optimizing capabilities of word-length optimization are studied. Application of the proposed procedure to adaptive filters and polynomial evaluation circuits realized in a Xilinx Virtex FPGA has resulted in area reductions of up to 80% (mean 66%) combined with power reductions of up to 98% (mean 87%) and speed-up of up to 36%(mean 20%) over common alternative design strategies.