光栅数字细分的CORDIC算法总量化误差分析

Analysis of the Overall Quantization Error for CORDIC Algorithm in Grating Digital Subdivision

针对光栅数字细分的CORDIC算法总量化误差EOQ进行了研究，根据CORDIC算法的基本原理进行了仿真和电路实验，结果表明在不同位宽b条件下预测值EOQs与实验值EOQp的差值与迭代次数n成反比，n=12时两者差值为1．8×10^-4md，证明了EOQ对CORDIC算法在光栅数字细分角度运算中的误差表征的有效性。对影响EOQ的关键参数以及误差分量进行了量化分析，分析结果表明EOQ随着n和b的增大呈现减少的趋势，其中／2对EOQ的减小起决定性作用。电路测试结果显示当b维持不变，n每增一次，EOQ近似减小50％。获得了关于EOQ影响CORDIC算法角度计算的结论，对于光栅数字细分过程中的误差分析具有参考和实用价值。

The overall quantization error （ EOQ ） of CORDIC algorithm is discussed based on grating digital subdivision technique. Simulations and circuit experiments are conducted according to the basic principles of CORDIC. The result shows that the difference between predicted and experimental values is inversely proportional to the number of iteration （n） under the conditions of different binary width （b）. The difference between the two reaches 1.8 × 10-4rad, when n is equal to 12. It proves the effectiveness of the usage of EOQ to value the error of the algorithm in the calculation of angle. A quantitative analysis on error components and key parameters which influence the EOQ is presented. The result shows that the trend of EoQ becomes smaller with the increase of n and b, in which n plays a decisive role in the reduction of EoQ. Circuit test result shows that when the b remains unchanged, EoQ probably decreases by 50% with n adding once. The paper concludes the impact on the angle calculation based on CORDIC caused by Eoq. The conclusion has important significance and practical value to the error analysis in the process of digital subdividing for grating.