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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 Refinable function ： ウィキペディア英語版 Refinable function In mathematics, in the area of wavelet analysis, a refinable function is a function which fulfils some kind of self-similarity. A function $\backslash varphi$ is called refinable with respect to the mask $h$ if :$\backslash varphi(x)=2\backslash cdot\backslash sum\_^\; h\_k\backslash cdot\backslash varphi(2\backslash cdot\; x-k)$ This condition is called refinement equation, dilation equation or two-scale equation. Using the convolution (denoted by a star, *) of a function with a discrete mask and the dilation operator $D$ one can write more concisely: :$\backslash varphi=2\backslash cdot\; D\_\; (h$ * \varphi) It means that one obtains the function, again, if you convolve the function with a discrete mask and then scale it back. There is a similarity to iterated function systems and de Rham curves. The operator $\backslash varphi\backslash mapsto\; 2\backslash cdot\; D\_\; (h$ * \varphi) is linear. A refinable function is an eigenfunction of that operator. Its absolute value is not uniquely defined. That is, if $\backslash varphi$ is a refinable function, then for every $c$ the function $c\backslash cdot\backslash varphi$ is refinable, too. These functions play a fundamental role in wavelet theory as scaling functions. ==Properties== 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「Refinable function」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.