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传统上都采用“乘加算术”实现正交变换，鲁棒性差。该文基于新的快速“旋转算术”，提出了各种正交变换包括重叠正交变换快速分解算法与运算结构。它们可以结合使用，将各种正交变换快速分解为Ｇｉｖｅｎｓ旋转序列，用快速旋转器硬件有效地进行运算，使整个变换所需“右移—加”运算次数大大减少，以至于其计算复杂度与传统的“乘加算术”可比，从而可以用在一类新型的以快速旋转器为内核实现各种正交变换的ＶＬＳＩ微处理器中。为此还按照所提出的算法开发了一个与微处理器相应的、能够产生高效控制代码的编译器。
Traditionally, “multiply-add arithmetic” is used to realize the orthogonal transform, which has poor robustness. Based on the new fast “Rotation Arithmetic”, this paper presents various orthogonal transformations, including the fast orthogonal decomposition decomposition algorithm and the operation structure. They can be used in combination to quickly decompose a variety of orthogonal transformations into Givens rotation sequences and efficiently operate with fast rotator hardware so that the number of “right-shift-add” operations required for the entire transformation is greatly reduced so that its computational complexity Comparing with the traditional “multiply-add arithmetic”, it can be used in a new type of VLSI microprocessor which realizes various orthogonal transformations with fast rotator. According to the proposed algorithm, a microprocessor-based compiler that generates efficient control code has also been developed for this purpose.