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The graph of a Gaussian is a characteristic symmetric "bell curve" shape. The parameter a is the height of the curve's peak, b is the position of the center of the peak, and c (the standard deviation, sometimes called the Gaussian RMS width) controls the width of the "bell".
In the physics of gas molecules, the root-mean-square speed is defined as the square root of the average squared-speed. The RMS speed of an ideal gas is calculated using the following equation: v RMS = 3 R T M {\displaystyle v_{\text{RMS}}={\sqrt {3RT \over M}}}
Full width at half maximum. 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 bioinformatics, the root mean square deviation of atomic positions is the measure of the average distance between the atoms of superimposed proteins. In structure based drug design , the RMSD is a measure of the difference between a crystal conformation of the ligand conformation and a docking prediction.
The Gaussian function has a 1/e 2 diameter (2w as used in the text) about 1.7 times the FWHM.. At a position z along the beam (measured from the focus), the spot size parameter w is given by a hyperbolic relation: [1] = + (), where [1] = is called the Rayleigh range as further discussed below, and is the refractive index of the medium.
The confined Gaussian window yields the smallest possible root mean square frequency width σ ω for a given temporal width (N + 1) σ t. [49] These windows optimize the RMS time-frequency bandwidth products. They are computed as the minimum eigenvectors of a parameter-dependent matrix.
Gaussian measures with mean = are known as centered Gaussian measures. The Dirac measure δ μ {\displaystyle \delta _{\mu }} is the weak limit of γ μ , σ 2 n {\displaystyle \gamma _{\mu ,\sigma ^{2}}^{n}} as σ → 0 {\displaystyle \sigma \to 0} , and is considered to be a degenerate Gaussian measure ; in contrast, Gaussian measures with ...
In telecommunications, maximum-ratio combining (MRC) is a method of diversity combining in which: the signals from each channel are added together, the gain of each channel is made proportional to the rms signal level and inversely proportional to the mean square noise level in that channel. different proportionality constants are used for each ...