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Full Width at Half Maximum


The full width at half maximum (FWHM) is a parameter commonly used to describe the width of a "bump" on a curve or function. It is given by the distance between points on the curve at which the function reaches half its maximum value. The following table gives the analytic and numerical full widths for several common curves.

functionformulaFWHM
Bartlett1-(|x|)/aa
Blackman0.810957a
Connes(1-(x^2)/(a^2))sqrt(4-2sqrt(2))a
cosinecos((pix)/(2a))4/3a
Gaussiane^(-x^2/(2sigma^2))2sqrt(2ln2)sigma
Hamming1.05543a
Hanninga
Lorentzian(1/2Gamma)/(x^2+(1/2Gamma)^2)Gamma
Welch1-(x^2)/(a^2)sqrt(2)a

See also

Apodization Function, Maximum

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Cite this as:

Weisstein, Eric W. "Full Width at Half Maximum." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/FullWidthatHalfMaximum.html

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