In this work, we proposed a novel Coordinate Rotation DIgital Computer (CORDIC) rotator algorithm that converges faster by performing radix-2,4 and 16 CORDIC iterations while maintaining the scale factor implicitly constant. A mixed-radix is used to achieve convergence faster to reduce the computational latency of the CORDIC algorithm. The main concern of the higher radix CORDIC algorithm is the compensation of a variable scale factor. To solve this problem, the Taylor series approximation of sine and cosine is proposed for a higher radix CORDIC algorithm to achieve the scaling-free rotation of the two-dimensional vector. The scaling-free rotation of the proposed CORDIC algorithm removes the read-only memory (ROM) needed to store scale factor of higher radix CORDIC algorithm. Further, the proposed CORDIC algorithm is designed in rotation mode and optimized by removing the Z datapath for the digital signal processing (DSP) applications for which the angle of rotation is known in advance. Finally, the multipath delay commutator (MDC) fast Fourier transform (FFT) algorithm is implemented with the proposed CORDIC algorithm based rotator on FPGA. The proposed design is compared with existing designs. In a comparison between the radix-16 CORDIC rotator based FFT implementation and our proposed implementation, it has been found out that implementation proposed in this article has used 17% fewer resources.

在这项工作中，我们提出了一种新颖的坐标旋转数字计算机（CORDIC）旋转器算法，该算法通过执行基数为2,4和16的CORDIC迭代而收敛得更快，同时保持比例因子隐式恒定。混合基数用于更快地收敛，以减少CORDIC算法的计算延迟。高基数CORDIC算法的主要关注点是可变比例因子的补偿。为了解决这个问题，正弦和余弦的泰勒级数逼近提出了一种针对更高基数的CORDIC算法，以实现二维矢量的无标度旋转。提出的CORDIC算法的无标度旋转消除了存储较高基数CORDIC算法的比例因子所需的只读存储器（ROM）。此外，提出的CORDIC算法以旋转模式设计，并通过删除Z数据路径进行了优化，以用于预先知道旋转角度的数字信号处理（DSP）应用。最后，在FPGA上基于CORDIC算法的旋转器实现了多径延迟换向器（MDC）快速傅里叶变换（FFT）算法。将拟议的设计与现有设计进行比较。在基于radix-16 CORDIC转子的FFT实现与我们提出的实现之间的比较中，资源减少％。