An angle recoding scheme for efficient realization of rotation-based digital signal processing algorithms

The CORDIC (coordinate rotation digital computer) algorithm is an iterative arithmetic procedure for generalized vector rotations. For applications where the angle of rotation is known in advance, it is possible to reduce the number of iterations through a technique (called angle recoding) in which the desired angle of rotation is encoded as a linear combination of very few elementary rotation angles. Unfortunately, an optimal encoding requires exhaustive search of exponentially growing number of possible combinations of these elementary angles. A Greedy algorithm which takes only O(n ²) operations was developed. It is proved that this algorithm is able to reduce the total number of elementary rotation angles by at least 50%. In the linear rotation case, it is shown that this proposed angle recoding scheme is equivalent to that of the modified Booth´s recoding method. Potential applications of the angle recoding scheme to a number of rotation based digital signal processing algorithms are discussed