Dirac delta function
pseudo-function δ such that an integral of δ(x-c)f(x) always takes the value of f(c)
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The Dirac delta function, often written as , is a made-up concept by mathematician Paul Dirac. It is a really pointy and skinny function that pokes out a point along a wave. Loosely speaking, it has the value of zero everywhere except at , in such a way that the area between the function and the x-axis adds up to 1.[1] The delta function is often used in sampling theory, where its pointiness is useful for getting clean samples.
![](http://upload.wikimedia.org/wikipedia/commons/thumb/4/48/Dirac_distribution_PDF.svg/325px-Dirac_distribution_PDF.svg.png)
![](http://upload.wikimedia.org/wikipedia/commons/b/b4/Dirac_function_approximation.gif)
The integral of the Dirac delta function is the Heaviside function. The Dirac delta function can be seen as the derivative of the Heaviside function. [2]
Related pages
changeReferences
change- ↑ "List of Calculus and Analysis Symbols". Math Vault. 2020-05-11. Retrieved 2020-10-06.
- ↑ Weisstein, Eric W. "Delta Function". mathworld.wolfram.com. Retrieved 2020-10-06.