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.
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 normal distribution of the form
where is the standard deviation and can be any value (the width of the function does not depend on translation), then the relationship between FWHM and the standard deviation is
Another important distribution function, related to solitons in optics, is the hyperbolic secant:
Any translating element was omitted, since it does not affect the FWHM. For this impulse we have:
where arsech is the inverse hyperbolic secant.
Famous quotes containing the words full, width and/or maximum:
“After us they’ll fly in hot air balloons, coat styles will change, perhaps they’ll discover a sixth sense and cultivate it, but life will remain the same, a hard life full of secrets, but happy. And a thousand years from now man will still be sighing, “Oh! Life is so hard!” and will still, like now, be afraid of death and not want to die.”
—Anton Pavlovich Chekhov (1860–1904)
“Newly stumbling to and fro
All they find, outside the fold,
Is a wretched width of cold.”
—Philip Larkin (1922–1986)
“Only at his maximum does an individual surpass all his derivative elements, and become purely himself. And most people never get there. In his own pure individuality a man surpasses his father and mother, and is utterly unknown to them.”
—D.H. (David Herbert)