Function Centroid
FunctionCentroid
By analogy with the geometric centroid, the centroid of an arbitrary function f(x) is defined as
where the integrals are taken over the domain of f(x). For example, for the Gaussian function f(x)=e^(-(x-x_0)^2/(2sigma^2)), the centroid is
If f(x) is normalized so that
| [画像: intf(x)dx=1, ] |
(3)
|
then its centroid is equivalent to its mean.
See also
Geometric Centroid, Mean, Triangle CentroidExplore with Wolfram|Alpha
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References
Bracewell, R. The Fourier Transform and Its Applications, 3rd ed. New York: McGraw-Hill, pp. 139-140 and 156, 1999.Referenced on Wolfram|Alpha
Function CentroidCite this as:
Weisstein, Eric W. "Function Centroid." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/FunctionCentroid.html