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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 Prony's method ： ウィキペディア英語版 Prony's method Prony analysis (Prony's method) was developed by Gaspard Riche de Prony in 1795. However, practical use of the method awaited the digital computer.〔Hauer, J.F. et al. (1990). "Initial Results in Prony Analysis of Power System Response Signals". ''IEEE Transactions on Power Systems'', 5, 1, 80-89.〕 Similar to the Fourier transform, Prony's method extracts valuable information from a uniformly sampled signal and builds a series of damped complex exponentials or sinusoids. This allows for the estimation of frequency, amplitude, phase and damping components of a signal. == The method == Let $f(t)$ be a signal consisting of $N$ evenly spaced samples. Prony's method fits a function :$\backslash hat(t)\; =\; \backslash sum\_^\; A\_i\; e^\; \backslash cos(2\backslash pi\; f\_i\; t\; +\; \backslash phi\_i)$ to the observed $f(t)$. After some manipulation utilizing Euler's formula, the following result is obtained. This allows more direct computation of terms. :$$ \begin \hat(t) &= \sum_^ A_i e^ \cos(2\pi f_i t + \phi_i) \\ &= \sum_^ \frac A_i e^e^ \end where: *$\backslash lambda\_i\; =\; \backslash sigma\_i\; \backslash pm\; j\; \backslash omega\_i$ are the eigenvalues of the system, *$\backslash sigma\_i$ are the damping components, *$\backslash phi\_i$ are the phase components, *$f\_i$ are the frequency components, *$A\_i$ are the amplitude components of the series, and *$j$ is the imaginary unit ($j^2\; =\; -1$). 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「Prony's method」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.