In a distribution, full width at half maximum (FWHM) is the difference between the two 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 if the function is symmetric. The term full duration at half maximum (FDHM) is preferred when the independent variable is time. 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 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 or, more specifically, half-power bandwidth. When half-power point is applied to antenna beam width, it is called half-power beam width. Gaussian beam#Beam waist If the considered function is the density of a normal distribution of the form where σ is the standard deviation and x0 is the expected value, then the relationship between FWHM and the standard deviation is The corresponding area within this FWHM accounts to approximately 76%. The width does not depend on the expected value x0; it is invariant under translations. If the FWHM of a Gaussian function is known, then it can be integrated by simple multiplication. 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 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.

About this result
This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.
Related lectures (3)
Gaussian Wave Packets: Theory and Applications
Explores Gaussian wave packets theory, focusing on their propagation and applications in different potentials.
Quantum mechanical modification of Lorentz Model: Doppler Broadening
Covers laser basics, electron oscillator model, absorption, refractive index, Bohr model, causality, Kramers-Kronig relation, damping, quantum vs classical views, and Doppler broadening.
Show more
Related publications (5)

New architecture for the analog front-end of Medipix4

Jean-Michel Sallese, Adil Koukab, Viros Sriskaran

The Medipix4 chip is the latest member of the family of Medipix pixel detector readout chips aimed at high rate spectroscopic X-ray imaging. Unlike its predecessors, it will be possible to tile the chip on all 4 sides permitting seamless large area coverag ...
ELSEVIER2020

Defect Passivation via the Incorporation of Tetrapropylammonium Cation Leading to Stability Enhancement in Lead Halide Perovskite

Anurag Krishna

Improving the performances of photovoltaic (PV) devices by suppressing nonradiative energy losses through surface defect passivation and enhancing the stability to the level of standard PV represents one critical challenge for perovskite solar cells. Here, ...
WILEY-V C H VERLAG GMBH2020

Prospection sur les images numériques proche infrarouge

Gilles Gachet

Introduction Les caméras multispectrales - Caractéristiques (tableau comparatif) Analyse du bruit (entropie) Analyse de la résolution effective (Full Width of edge response at Half Height) Comparaison des résolutions spatiales Formats de compression Rehaus ...
2006
Show more
Related concepts (1)
Spectroscopy
Spectroscopy is the field of study that measures and interprets the electromagnetic spectra that result from the interaction between electromagnetic radiation and matter as a function of the wavelength or frequency of the radiation. Matter waves and acoustic waves can also be considered forms of radiative energy, and recently gravitational waves have been associated with a spectral signature in the context of the Laser Interferometer Gravitational-Wave Observatory (LIGO).