查看“︁半峰全宽”︁的源代码

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[[Image:FWHM.svg|thumb|250px|right|半高宽]]

'''半峰全宽'''（{{lang-en|Full width at half maximum}}，缩写为FWHM），也称作半高全宽、半峰全幅、或半高寬。是指在函数的一个峰当中，前后两个函数值等于峰值一半的点之间的距离。通常在[[光学]]、光学[[电信|通信]]、[[频谱]]学中用来描述[[譜線]]、[[辐射功率]]。如果自变量是时间，通常使用半幅值脉宽 （full duration at half maximum，缩写为FDHM）这一概念。

它可以用来计算[[高斯函数]]的积分。高斯函数的半峰全宽为<math> \mathrm{FWHM} =   2\sqrt{2 \ln 2 } \; \sigma \approx 2.355 \; \sigma</math>，其中<math>\sigma</math>为[[標準差]]。<ref>{{Cite web|title=What is Full Width at Half Maximum (FWHM)? - StellarNet, Inc.|url=https://www.stellarnet.us/what-is-full-width-at-half-maximum-fwhm/|accessdate=2020-05-17|work=www.stellarnet.us|archive-date=2017-08-18|archive-url=https://web.archive.org/web/20170818162437/http://www.stellarnet.us/what-is-full-width-at-half-maximum-fwhm/|dead-url=no}}</ref>

==數學應用==
{| class="wikitable"
|-
! 函數 !! 公式 !! FWHM
|-
| [[窗函数#Bartlett窗（端点值为0）|Bartlett]] || <math>1-\frac{\mid x \mid}{a}</math> || a
|-
| [[窗函数#Blackman窗|Blackman]] ||  || 0.810957a
|-
| [[cosine]] || <math>\cos(\frac{\pi x}{2a})</math> || <math>\frac{4}{3}</math>a
|-
| [[窗函数#高斯窗|Gaussian]] || <math>\exp(\frac{-x^2}{2\sigma^2})</math>|| <math>2\sqrt{2\ln2}\sigma</math>
|-
| [[窗函数#Hamming窗|Hamming]] ||  || 1.05543a
|-
| [[窗函数#Hann窗|Hanning]] ||  || a
|-
| [[Lorentzian]] || <math>\frac{\frac{1}{2}\Gamma}{x^2+(\frac{1}{2}\Gamma)^2}</math> || <math>\Gamma</math>
|-
| [[Welch]] || 1-<math>\frac{x^2}{a^2}</math> || <math>\sqrt{2}a</math>
|}
<ref>{{Cite mathworld|title=Full Width at Half Maximum|urlname=FullWidthatHalfMaximum|accessdate=2020-05-17|language=en|archive-date=2020-06-06|archive-url=https://web.archive.org/web/20200606170109/https://mathworld.wolfram.com/FullWidthatHalfMaximum.html|dead-url=no}}</ref>

==參考文獻==
{{Reflist}}

==外部連結==
*[https://www.stellarnet.us/what-is-full-width-at-half-maximum-fwhm/ 什麼是半峰全寬?]{{Wayback|url=https://www.stellarnet.us/what-is-full-width-at-half-maximum-fwhm/ |date=20170818162437 }}
*{{mathworld|urlname=FullWidthatHalfMaximum}}

{{Applied-math-stub}}

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