数字信号外文翻译--基于fpga的cordic算法综述(编辑修改稿)

数字信号外文翻译--基于fpga的cordic算法综述(编辑修改稿)内容摘要：

normally operated in one of two modes. The first, called rotation by Volder\[4], rotates the input vector by a specified angle (given as an argument). The second mode, called vectoring, rotates the input vector to the xaxis while recording the angle required to make that rotation. In rotation mode, the angle accumulator is initialized with the desired rotation angle. The rotation decision at each iteration is made to diminish the magnitude of the residual angle in the angle accumulator. The decision at each iteration is therefore based on the sign of the residual angle after each step. Naturally, if the input angle is already expressed in the binary arctangent base, the angle accumulator may be eliminated. For rotation mode, the CORDIC equations are: 1 2 ii i i ix x y d      1 2 ii i i iy y x d     11 ta n ( 2 )ii i iz z d     Where di=1 if zi0,+1 otherwise Which provides the following result: 0 0 0 0[ c o s s in ]nnx A x z y z 0 0 0 0[ c o s s in ]nny A y z x z 0nz 212innA   In the vectoring mode, the CORDIC rotator rotates the input vector through whatever angle is necessary to align the result vector with the x axis. The result of the vectoring operation is a rotation angle and the scaled magnitude of the original vector (the x ponent of the result). The vectoring function works by seeking to minimize the y ponent of the residual vector at each rotation. The sign of the residual y ponent is used to determine which direction to rotate next. If the angle accumulator is initialized with zero, it will contain the traversed angle at the end of the iterations. In vectoring mode, the CORDIC equations are: 1 2 ii i i ix x y d      1 2 ii i i iy y x d     11 ta n ( 2 )ii i iz z d     Where di=+1 if yi0,1 otherwise Then: 2200nnx A x y 0ny 10 0 0ta n ( / )nz z y x 212innA   The CORDIC rotation and vectoring algorithms as stated are limited to rotation angles between π/2 and π/2. This limitation is due to the use of 20 for the tangent in the first iteration. For posite rotation angles larger than π/2, an additional rotation is required. Volder\[4] describes an initial rotation 177。 π/2. This gives the correction iteration: 39。 x d y  39。 y d x 39。 / 2z z d    Where di=+1 if yi0,1 otherwise There is no growth for this initial rotation. Alternatively, an initial rotation of either π or 0 can be made, avoiding the reassignment of the x and y ponents to the rotator elements. Again, there is no growth due to the initial rotation:。