The quantization effects of the CORDIC algorithm (coordinate rotation digital computer)

摘要

CORDIC is a rotation-based arithmetic computing algorithm which has many important signal processing applications. Quantization errors occurring in the CORDIC algorithm are analyzed. Two types of quantization errors in the CORDIC algorithm are identified: one is an approximation error due to a quantized representation of rotation angles; another is the rounding error due to finite-precision arithmetic. Tight error bounds for these two types of errors are derived for both fixed-point and floating-point arithmetic. The effect of scaling (normalization) has been taken into account. These theoretical results are verified by simulation examples. The impact of these results on the architecture of a practical CORDIC processor is discussed.