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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 Shannon wavelet ： ウィキペディア英語版 Shannon wavelet In functional analysis, a Shannon wavelet may be either of real or complex type. Signal analysis by ideal bandpass filters defines a decomposition known as Shannon wavelets (or sinc wavelets). The Haar and sinc systems are Fourier duals of each other. == Real Shannon wavelet == The Fourier transform of the Shannon mother wavelet is given by: : $\backslash Psi^(w)\; =\; \backslash prod\; \backslash left(\; \backslash frac\; \backslash right)+\backslash prod\; \backslash left(\; \backslash frac\; \backslash right).$ where the (normalised) gate function is defined by : $\backslash prod\; (\; x):=$ \begin 1, & \mbox , \\ 0 & \mbox \mbox. \\ \end The analytical expression of the real Shannon wavelet can be found by taking the inverse Fourier transform: : $\backslash psi^(t)\; =\; \backslash operatorname\; \backslash left(\; \backslash frac\; \backslash right)\backslash cdot\; \backslash cos\; \backslash left(\; \backslash frac\; \backslash right)$ or alternatively as : $\backslash psi^(t)=2\; \backslash cdot\; \backslash operatorname(2t\; -\; 1)-\backslash operatorname(t),$ where : $\backslash operatorname(t):=\; \backslash frac$ is the usual sinc function that appears in Shannon sampling theorem. This wavelet belongs to the $C^\backslash infty$-class of differentiability, but it decreases slowly at infinity and has no bounded support, since band-limited signals cannot be time-limited. The scaling function for the Shannon MRA (or ''Sinc''-MRA) is given by the sample function: : $\backslash phi^(t)=\; \backslash frac\; =\; \backslash operatorname(t).$ 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「Shannon wavelet」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.