“Gaussian Function”的概念、定义、习题解题方法及翻译-数学辞典

单词

Gaussian Function

释义

Gaussian Function

In 1-D, the Gaussian function is the function from the Gaussian Distribution,

(1)

sometimes also called the Frequency Curve. The Full Width at Half Maximum (FWHM) for a Gaussian is found byfinding the half-maximum points

. The constant scaling factor can be ignored, so we must solve

(2)

But

occurs at

, so

(3)

Solving,

(4)

(5)

(6)

(7)

The Full Width at Half Maximum is therefore given by

(8)

In 2-D, the circular Gaussian function is the distribution function for uncorrelated variables and having aGaussian Bivariate Distribution and equal Standard Deviation ,

(9)

The corresponding elliptical Gaussian function corresponding to

is given by

(10)

The above plots show the real and imaginary parts of together with the complex absolute value.

The Gaussian function can also be used as an Apodization Function, shown above with the correspondingInstrument Function.

The Hypergeometric Function is also sometimes known as the Gaussian function.

See also Erf, Erfc, Fourier Transform--Gaussian, Gaussian BivariateDistribution, Gaussian Distribution, Normal Distribution

References

MacTutor History of Mathematics Archive. ``Frequency Curve.''http://www-groups.dcs.st-and.ac.uk/~history/Curves/Frequency.html.

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