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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 Full width at half maximum ： ウィキペディア英語版 Full width at half maximum Full width at half maximum (FWHM) is an expression of the extent of a function given by the difference between the two extreme values of the independent variable at which the dependent variable is equal to half of its maximum value. In other words, it is the width of a spectrum curve measured between those points on the ''y''-axis which are half the maximum amplitude. Half width at half maximum (HWHM) is half of the FWHM. FWHM is applied to such phenomena as the duration of pulse waveforms and the spectral width of sources used for optical communications and the resolution of spectrometers. The term full duration at half maximum (FDHM) is preferred when the independent variable is time. The convention of "width" meaning "half maximum" is also widely used in signal processing to define bandwidth as "width of frequency range where less than half the signal's power is attenuated", i.e., the power is at least half the maximum. In signal processing terms, this is at most −3 dB of attenuation, called "half power point". If the considered function is the density of a normal distribution of the form :$f(x)\; =\; \backslash frac\; \backslash exp\; \backslash left(-\backslash frac\; \backslash right)$ where $\backslash sigma$ is the standard deviation and $x\_0$ is the expected value, then the relationship between FWHM and the standard deviation is〔(Gaussian Function - from Wolfram MathWorld )〕 :$\backslash mathrm\; =\; 2\backslash sqrt\; \backslash ;\; \backslash sigma\; \backslash approx\; 2.355\; \backslash ;\; \backslash sigma.$ The width does not depend on the expected value ''x''0; it is invariant under translations. In spectroscopy half the width at half maximum (here γ), HWHM, is in common use. For example, a Lorentzian/Cauchy distribution of height (1/πγ) can be defined by :$f(x)\; =\; \backslash frac\backslash right)^2\backslash right\; )\}\; \backslash text\; \backslash mathrm\; =\; 2\; \backslash gamma.$ Another important distribution function, related to solitons in optics, is the hyperbolic secant: :$f(x)=\backslash operatorname\; \backslash left(\; \backslash frac\; \backslash right).$ Any translating element was omitted, since it does not affect the FWHM. For this impulse we have: :$\backslash mathrm\; =\; 2\; \backslash ;\; \backslash operatorname\; \backslash left(\; \backslash frac\; \backslash right)\; X\; =\; 2\; \backslash ln\; (2\; +\; \backslash sqrt)\; \backslash ;\; X\; \backslash approx\; 2.634\; \backslash ;\; X$ where ''arsech'' is the inverse hyperbolic secant. == See also == *Gaussian function *Cutoff frequency 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「Full width at half maximum」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.