數(shù)字信號外文翻譯--基于fpga的cordic算法綜述-文庫吧在線文庫
【正文】 初始旋轉(zhuǎn)值都是可以的，這樣避免把 x和 y 分量調(diào)換為旋轉(zhuǎn)因子。恰當?shù)倪x擇初始值和模式可以直接計算正弦，余弦，反正切，矢量幅度以及極坐標和直角坐標之間的轉(zhuǎn)換。 CORDIC 算法是在 DSP 家族中的強大工具。然后，我們用最簡單和最復雜的硬件來實現(xiàn)要求。=z 或者如果 d=1,z39。這樣就給出了正確的迭代方程： 39。向 量運算是通過找到在每次旋轉(zhuǎn)后 y 分量的冗余向量的最小值來運算的。第一種模式，稱為旋轉(zhuǎn)模式，通過一個特殊角度（作為參數(shù)提供）旋轉(zhuǎn)輸入的向量。該序列被向量所代表。通過一系列連續(xù)的小角度旋轉(zhuǎn)便可得到任意角度的旋轉(zhuǎn)。矢量旋轉(zhuǎn)也可用于極坐標和直角坐標的相互轉(zhuǎn)換，矢量大小以及某些諸如的 DFT 和 DCT的變換。不幸的是，這些基于微處理器的系統(tǒng)通常不能很好地把算法優(yōu)化映射到硬件中去。s hardware DSP designs are being done by engineers with little or no background in hardware efficient DSP algorithms. The new DSP designers must bee familiar with these algorithms and the techniques for implementing them in FPGAs in order to remain petitive. The CORDIC algorithm is a powerful tool in the DSP toolbox. This paper shows that tool is available for use in FPGA based puting machines, which are the likely basis for the next generation DSP systems. 基于 FPGA 的 CORDIC 算法綜述 目前趨向于硬件的信號處理卻缺乏對硬件信號處理結(jié)構(gòu)的理解。s can be applied elsewhere in the system or treated as part of a system processing gain. That product approaches as the number of iterations goes to infinity. Therefore, the rotation algorithm has a gain, An , of approximately . The exact gain depends on the number of iterations, and obeys the relation. 212innA ??? ? The angle of a posite rotation is uniquely defined by the sequence of the directions of the elementary rotations. That sequence can be represented by a decision vector. The set of all possible decision vectors is an angular measurement system based on binary arctangents. Conversions between this angular system and any other can be acplished using a lookup. A better conversion method uses an additional addersubtractor that accumulates the elementary rotation angles at each iteration. The elementary angles can be expressed in any convenient angular unit. Those angular values are supplied by a small lookup table (one entry per iteration) or are hardwired, depending on the implementation. The angle accumulator adds a third difference equation to the CORDIC algorithm: 11 ta n ( 2 )ii i iz z d ??? ? ? ? Obviously, in cases where the angle is useful in the arctangent base, this extra element is not needed. The CORDIC rotator is 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
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