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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 Linear response function ： ウィキペディア英語版 Linear response function A linear response function describes the input-output relationship of a signal transducer such as a radio turning electromagnetic waves into music or a neuron turning synaptic input into a response. Because of its many applications in information theory, physics and engineering there exist alternative names for specific linear response functions such as susceptibility, impulse response or impedance, see also transfer function. The concept of a Green's function or fundamental solution of an ordinary differential equation is closely related. ==Mathematical definition== Denote the input of a system by $h(t)$ (e.g. a force), and the response of the system by $x(t)$ (e.g. a position). Generally, the value of $x(t)$ will depend not only on the present value of $h(t)$, but also on past values. Approximately $x(t)$ is a weighted sum of the previous values of $h(t\text{'})$, with the weights given by the linear response function $\backslash chi(t-t\text{'})$: :$x(t)=\backslash int\_^t\; dt\text{'}\backslash ,\; \backslash chi(t-t\text{'})h(t\text{'})+\backslash dots\backslash ,.$ The explicit term on the r.h.s. is the leading order term of a Volterra expansion for the full nonlinear response. If the system in question is highly non-linear, higher order terms in the expansion, denoted by the dots, become important and the signal transducer can not adequately be described just by its linear response function. The complex-valued Fourier transform $\backslash tilde(\backslash omega)$ of the linear response function is very useful as it describes the output of the system if the input is a sine wave $h(t)=h\_0\backslash cdot\; \backslash sin(\backslash omega\; t)$ with frequency $\backslash omega$. The output reads :$x(t)=|\backslash tilde(\backslash omega)|\backslash cdot\; h\_0\; \backslash cdot\backslash sin(\backslash omega\; t+\backslash arg\backslash tilde(\backslash omega))\backslash ,,$ with amplitude gain $|\backslash tilde(\backslash omega)|$ and phase shift $\backslash arg\backslash tilde(\backslash omega)$. 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「Linear response 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.