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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Number theoretic Hilbert transform ： ウィキペディア英語版 Number theoretic Hilbert transform The number theoretic Hilbert transform is an extension〔 * 〕 of the discrete Hilbert transform to integers modulo a prime $p$. The transformation operator is a circulant matrix. The number theoretic transform is meaningful in the ring $\backslash mathbb\_m$, when the modulus $m$ is not prime, provided a principal root of order ''n'' exists. The $n\backslash times\; n$ NHT matrix, where $n\; =2m$, has the form :$$ NHT= \begin 0 & a_ & \dots & 0 & a_ \\ a_ & 0 & a_ & & 0 \\ \vdots & a_& 0 & \ddots & \vdots \\ 0 & & \ddots & \ddots & a_ \\ a_ & 0& \dots & a_ & 0 \\ \end. The rows are the cyclic permutations of the first row, or the columns may be seen as the cyclic permutations of the first column. The NHT is its own inverse:$NHT^\backslash mathrm\; NHT\; =\; NHT\; NHT^\backslash mathrm\; =\; I\; \backslash bmod\backslash \; p,\; \backslash ,$ where ''I'' is the identity matrix. The number theoretic Hilbert transform can be used to generate sets of orthogonal discrete sequences that have applications in signal processing, wireless systems, and cryptography.〔 ()〕 Other ways to generate constrained orthogonal sequences also exist.〔Donelan, H. (1999). Method for generating sets of orthogonal sequences. Electronics Letters 35: 1537-1538.〕〔Appuswamy, R., Chaturvedi, A.K. (2006). A new framework for constructing mutually orthogonal complementary sets and ZCZ sequences. IEEE Trans. Information Theory 52: 3817-3826.〕 ==References== 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Number theoretic Hilbert transform」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.