High-radix CORDIC for vector rotation with pipelined FPGA implementation

We present a new, mixed-radix (radix-4/radix-2) CORDIC algorithm for vector rotation and an efficient, pipelined implementation in Atmel´s AT40K technology. Using only 3 radix-4 stages and one radix-2 stage, a sample rotator using this new algorithm achieves in 4 clock cycles the same accuracy that a conventional (radix-2) rotator would achieve in 7 cycles, while each cycle is almost the same speed as that of a conventional rotator. This sample rotator attains 12 bits of accuracy externally, while internally 17 bits of accuracy is kept. This rotator fits in an AT40K30, and has a worst-case delay of up to 55.9 ns per stage (speed level 2) and a typical delay of 35 ns including output buffers. CORDIC rotators can be used to improve the efficiency of many important DSP functions such as transforms, modulation and demodulation, motion sensing and control, and image processing