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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 Spectrum continuation analysis ： ウィキペディア英語版 Spectrum continuation analysis Spectrum continuation analysis (SCA) is a generalization of the concept of Fourier series to non-periodic functions of which only a fragment has been sampled in the time domain. Recall that a Fourier series is only suitable to the analysis of periodic (or finite-domain) functions ''f''(''x'') with period 2π. It can be expressed as an infinite series of sinusoids: :$f(x)\; =\; \backslash sum\_^\; F\_n\; \backslash ,e^$ where $F\_n$ is the amplitude of the individual harmonics. In SCA however, one decomposes the spectrum into optimized discrete frequencies. As a consequence, and as the period of the sampled function is supposed to be infinite or not yet known, each of the discrete periodic functions that compose the sampled function fragment can not be considered to be a multiple of the fundamental frequency: :$f(x)\; =\; \backslash sum\_^\; F\_n\; \backslash ,e^.$ As such, SCA does not necessarily deliver $2\; \backslash pi$ periodic functions, as would have been the case in Fourier analysis. For real-valued functions, the SCA series can be written as: :$f(x)\; =\; \backslash sum\_^\backslash infty\backslash left(\backslash cos(\backslash omega\_n\; x)+B\_n\; \backslash sin(\backslash omega\_n\; x)\backslash right)\; +\; C(x)$ where ''A''''n'' and ''B''''n'' are the series amplitudes. The amplitudes can only be solved if the series of values $\backslash omega\_n$ is previously optimized for a desired objective function (usually least residuals). $C(x)$ is not necessarily the average value over the sampled interval: one might prefer to include predominant information on the behavior of the offset value in the time domain. ==Etymology== SCA deals with the prediction problem of continuing a frequency spectrum beyond a sampled (usually stochastic) time series fragment. Unlike ordinary Fourier analysis that infinitely repeats an observed function period or time domain, SCA filters the exact composing frequencies out of the observed spectrum and let them continue (resp. precede) in the time domain. In the scientific terminology, therefore preference is given to the term ''continuation'' rather than for instance ''extrapolation''. 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「Spectrum continuation analysis」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.