文档介绍：涂娟:反夹克变换、夹克矩阵的构造与应用
中文摘要
央克矩阵的基本思想是出于对夹克上衣布料的考虑,由于我们的双面央克外套是内外兼容的。一个夹克矩阵至少有两个位置被它们的逆所替代,这些元素在其位置被移动从而改变它们的位置。比如:从中圈的里面到外面或从外面到里面而没有符号损失。
夹克矩阵作为wHT和DFT的推广,近些年关于夹克矩阵以及其对应的一些变换被广泛的研究和报告,除了在数学和物理问题上有很多应用之外,更多的被应用于信号处理、信息论与编码理论、图象编码与压缩、CDMA通信、量子信息、密码学等等。因夹克矩阵结构简单且是可逆的,其逆矩阵很易得到,它的算法相对简单以使它成为研究的热门方向。 CWHT和CRJT在应用上可取代WHT和DFT作为后者的推广,在此基础上又有了更一般的GRJT。他们可应用于更多的领域,范围更广阔。其优势备受人们关注。
本章首先简单介绍哈达马矩阵以及离散傅里叶变换(简称DFT)的概念以及其在通信领域中的应用。接着给出了夹克矩阵定义、夹克矩阵带来的好处以及其研究进展。然后利用张量积用小阶的反夹克矩阵和哈达马矩阵来构造更大阶的反夹克矩阵,同时得到构造反夹克矩阵和其逆矩阵的一般公式。在复数域上构造夹克矩阵及在已有的夹克矩阵构造方法基础得出一般的范德蒙德矩阵并证明其为夹克矩阵。接下来列举出夹克矩阵、A、编码、信号处理中的应用。最后对本文进行总结以及前景展望。
关键字:夹克矩阵反夹克变换哈达马矩阵斐波那契数M-序列
扬州大学硕士学位论文 2
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Abstract
Jacket matrix basic idea was motivated by the cloths of our two sided Jacket is inside and patible,at least two positions of a Jacket matrix ar e replaced by their inverse;these elements are changed in their position and are moved,for example,from inside of the middle circle to outside or from to inside without loss of sign。
The Walsh-Hadamard transform(WHT)and discrete Fourier transform(DFT)are widelv used in signal particular,these transforms ar e used in image coding and processing and error-control of these two transforms。called the center
weighted Hadamard transform(CWHT)and plex reverse jacket transform(CRJT)have
been jacket transform is SO named because it brings to mind a . Just as the jacket is easily reversed(turned inside out),SO too the jacket matrix is easily inverted. The CWHT and CRJT Can be seen as generalizations ofthe wHT.
This paper first has simply introduced hadamard matrices and discrete fourier transform, which are widely used in signal processing,in particular,these transform are used in image coding and processing and error-control ,we will talk about the definition of jacket matrix and its advantage and research use Krone