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首页> 外文期刊>IEEE transactions on circuits and systems . I , Regular papers >A Generalized Reverse Block Jacket Transform
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A Generalized Reverse Block Jacket Transform

机译：广义逆向块夹克变换

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摘要

Jacket matrices motivated by the center weight Hadamard matrices have played important roles in signal processing, communication, image compression, cryptography, etc. In this paper we propose a notation called block Jacket matrix which substitutes elements of the matrix into common matrices or even block matrices. Employing the well-known Pauli matrices which are very important in many subjects, block Jacket matrices with any size are investigated in detail, and some recursive relations for fast construction of the block Jacket matrices are obtained. Based on the general recursive relations, several special block Jacket matrices are constructed. To decompose high order block Jacket matrices, a fast decomposition algorithm for the factorable block Jacket matrices is suggested. After that some properties of the block Jacket matrices are investigated. Finally, several remarks are presented. These remarks are associated with comparisons between the Clifford algebra and the block Jacket matrices, generations of orthogonal and quasi-orthogonal sequences, and relations of the block Jacket matrices to the orthogonal transforms for signal processing. Since the Pauli matrices are actually infinitesimal generators of $SU(2)$ group, the proposed construction and decomposition algorithms for the block Jacket matrices are available in the signal processing, communication, quantum signal processing and information theory.
机译：以中心权重Hadamard矩阵为动力的Jacket矩阵在信号处理，通信，图像压缩，密码学等方面起着重要作用。在本文中，我们提出了一种称为Block Jacket矩阵的表示法，它将矩阵中的元素替换为常见矩阵甚至是Block矩阵。 。利用在许多学科中都非常重要的著名保利矩阵，详细研究了任意大小的块护套矩阵，并获得了一些快速构造块护套矩阵的递归关系。基于一般的递归关系，构造了几种特殊的块夹克矩阵。为了分解高阶块Jacket矩阵，提出了一种可分解​​块Jacket矩阵的快速分解算法。此后，研究块夹克矩阵的某些属性。最后，提出了一些意见。这些说明与Clifford代数与块Jacket矩阵之间的比较，正交和准正交序列的生成以及块Jacket矩阵与用于信号处理的正交变换之间的关系有关。由于Pauli矩阵实际上是$ SU（2）$组的无穷小生成器，因此在信号处理，通信，量子信号处理和信息论中都可以使用针对块Jacket矩阵提出的构造和分解算法。

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