An analysis of the CORDIC algorithm for direct digital frequency synthesis

The circular-mode CORDIC (coordinate rotation digital computer) algorithm is analyzed for DDFS (direct digital frequency synthesis) applications. It is shown how the CORDIC parameters should be chosen to meet given DDFS parameters. Also, three methods of CORDIC datapath quantization: rounding, truncation, and jamming, have been investigated and their error bounds are derived. Through a set of simulations, it is demonstrated that jamming has desirable characteristics in many aspects such as complexity, speed, error, and bias. Finally, it is shown that the CORDIC output can be made exact to the digits by an additional rounding process, which is especially useful for DDFS applications where the CORDIC output should be truncated to the final DAC (digital-to-analog converter) width.