CORDIC Algorithms and Architectures Herbert Dawid Heinrich

Digital signal processing (DSP) algorithms exhibit an increasing need for the e cient implementation of complex arithmetic operations. The computation of trigonometric functions, coordinate transformations or rotations of complex valued phasors is almost naturally involved with modern DSP algorithms. Popular application examples are algorithms used in digital communication technology and in adaptive signal processing. While in digital communications, the straightforward evaluation of the cited functions is important, numerous matrix based adaptive signal processing algorithms require the solution of systems of linear equations, QR factorization or the computation of eigenvalues, eigenvectors or singular values. All these tasks can be e ciently implemented using processing elements performing vector rotations. The COordinate Rotation DIgital Computer algorithm (CORDIC) o ers the opportunity to calculate all the desired functions in a rather simple and elegant way. The CORDIC algorithm was rst introduced by Volder [1] for the computation of trigonometric functions, multiplication, division and datatype conversion, and later on generalized to hyperbolic functions by Walther [2]. Two basic CORDIC modes are known leading to the computation of di erent functions, the rotation mode and the vectoring mode. For both modes the algorithm can be realized as an iterative sequence of additions/subtractions and shift operations, which are rotations by a xed rotation angle (sometimes called microrotations) but with variable rotation direction. Due to the simplicity of the involved operations the CORDIC algorithm is very well