座標旋轉計算技術之改進

Abstract

在本論文裡探討了加速座標旋轉數位計算處理器的方法，包括使用多 餘數加法架構與應用布氏編碼之旋轉方向預測法等可以使運算平行度增加 之技術，還有線上比例因數分解補償演算法更可以用簡單的硬體架構來計 算可變數值之比例因數；並且根據這些改進的演算法設計了圓形座標系統 下旋轉模式之座標旋轉數位計算處理器架構，可用於計算三角函數中的正 弦函數與餘弦函數以及其他引伸之函數。此外並討論了如何應用座標旋轉 數位計算演算法於適應性信號處理上，提出了新的有效率之以座標旋轉數 位計算處理器為基礎的適應性晶格濾波器架構。 論文本文之結構如下 ：第一章介紹座標旋轉數位計算演算法的原理以及加速座標旋轉數位計算 的方法；第二章介紹了數種現有的快速座標旋轉數位計算演算法；第三章 中提出使用旋轉方向預測法配合線上比例因數分解補償演算法之改良的座 標旋轉數位計算演算法，並設計此座標旋轉數位計算處理器之架構；第四 章裡介紹使用偶數次旋轉序列計算雙曲線函數與反三角函數之演算法；第 五章則介紹了如何使用座標旋轉數位計算處理器設計適應性晶格濾波器， 並提出了數種改良之演算法與現有之演算法作一比較；第六章為結論，總 結目前研究的結果與尚待改進之問題，以指出未來可研究之方向。 In this thesis, techniques to improve the computation of Coordinate Rotation Digital Computer(CORDIC) are studied, including methods of increasing parallelism of computations by using the redundant number addition scheme and the rotation- direction factor prediction method based on the modified Booth encoding, as well as the on-line scale factor decomposition and compensation algorithm, which can deal with variable scale factors. The architecture of CORDIC processor for rotation mode under the circular coordinate system is also designed based on those refining algorithms. Besides, how to apply the CORDIC algorithm to adaptive signal processing is discussed, and new and computation-efficient architectures of adaptive lattice filter based on CORDIC processors are proposed. The organization of this thesis is as below: in Chapter 1, the basic principles of CORDIC is introduced and various methods to speedup the algorithm are also described; in Chapter 2, some kinds of existing fast CORDIC algorithms are introduced; in Chapter 3, a refined algorithm and architecture of CORDIC processor based on the rotation-direction factor prediction method and the on-line scale factor decomposition and compensation algorithm are proposed; in Chapter 4, algorithms of computing hyperbolic functions and inverse sine and cosine functions with even number shift sequences are proposed; in Chapter 5, some efficient algorithms of adaptive lattice filter based on CORDIC processors are proposed; Chapter 6 draws a conclusion and points out the future works.