New redundant CORDIC algorithms with fast variable scale factor compensations

Abstract

In this work, new redundant CORDIC algorithms based on a fast variable scale factor compensation algorithm are proposed. By decomposing the complicated variable scale factor /spl Pi/(1+/spl delta//sub i//sup 2/2/sup -2i/)/sup -0.5/ as Exp(-/spl Sigma/ln(1+/spl delta//sub i//sup 2/2/sup -2i/)/2), then in turn as /spl Pi/(1+s/sub i/2/sup -i/), where s/sub i//spl isin/{-1,0,1}, we can easily determine the direction factor /spl delta//sub i//spl isin/{-1,0,1}, and at the same time do variable scale factor compensation by simply performing shift-and-add operations. The value of s/sub i/ can be easily obtained by estimating only a few most-significant digits (MSD) value of an intermediate variable. The new redundant CORDICs achieve high speed rotation iterations, as well as high-speed and low-complexity scale factor compensations, which are hard to attain simultaneously by the existing redundant CORDICs with variable scale factors.