Impact-Site-Verification: dbe48ff9-4514-40fe-8cc0-70131430799e

## Search This Blog

Gaussian function, often simply referred to as a Gaussian, is a function of the form:

${\displaystyle f(x)=ae^{-{\frac {(x-b)^{2}}{2c^{2}}}}}$
for arbitrary real constants ab and c. It is named after the mathematician Carl Friedrich Gauss. 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".
Gaussian functions are often used to represent the probability density function of a normally distributed random variable with expected value Î¼ = b and variance Ïƒ2 = c2. In this case, the Gaussian is of the form:

${\displaystyle g(x)={\frac {1}{\sigma {\sqrt {2\pi }}}}e^{-{\frac {1}{2}}\left({\frac {x-\mu }{\sigma }}\right)^{2}}.}$
Gaussian functions are widely used in statistics to describe the normal distributions, in signal processing to define Gaussian filters, in image processing where two-dimensional Gaussians are used for Gaussian blurs, and in mathematics to solve heat equations and diffusion equations and to define the Weierstrass transform.