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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 Spectral concentration problem ： ウィキペディア英語版 Spectral concentration problem The spectral concentration problem in Fourier analysis refers to finding a time sequence whose discrete Fourier transform is maximally localized on a given frequency interval, as measured by the spectral concentration. ==Spectral concentration== The discrete-time Fourier transform (DTFT) ''U''(''f'') of a finite series $w\_t$, $t\; =\; 1,2,3,4,...,T$ is defined as :$U(f)\; =\; \backslash sum\_^w\_t\; e^.$ In the following, the sampling interval will be taken as Δ''t'' = 1, and hence the frequency interval as ''f'' ∈ (). ''U''(''f'') is a periodic function with a period 1. For a given frequency ''W'' such that 0<''W''<½, the spectral concentration $\backslash lambda(T,W)$ of ''U''(''f'') on the interval () is defined as the ratio of power of ''U''(''f'') contained in the frequency band () to the power of ''U''(''f'') contained in the entire frequency band (). That is, :$\backslash lambda(T,W)\; =\; \backslash frac\; ^2\; \backslash ,df\}\; ^2\; \backslash ,df\}.$ It can be shown that ''U''(''f'') has only isolated zeros and hence (see ()). Thus, the spectral concentration is strictly less than one, and there is no finite sequence $w\_t$ for which the DTFT can be confined to a band () and made to vanish outside this band. 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「Spectral concentration problem」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.