Dirac delta function

From TCS Wiki
Revision as of 12:07, 18 August 2017 by imported>Peterdownunder (Reverted 2 edits by 64.128.118.130 (talk) identified as vandalism to last revision by Dexbot. (TW))
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to navigation Jump to search
File:Dirac distribution PDF.svg
Schematic representation of the Dirac delta function by a line surmounted by an arrow. The height of the arrow is usually used to specify the value of any multiplicative constant, which will give the area under the function. The other convention is to write the area next to the arrowhead.
File:Dirac function approximation.gif
The Dirac delta function as the limit (in the sense of distributions) of the sequence of zero-centered normal distributions [math]\displaystyle{ \delta_a(x) = \frac{1}{a \sqrt{\pi}} \mathrm{e}^{-x^2/a^2} }[/math] as [math]\displaystyle{ a \rightarrow 0 }[/math].

The Dirac delta function 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. The delta function is used a lot in sampling theory where its pointiness is useful for getting clean samples.

The integral of the Dirac Delta Function is the Heaviside Function.

Template:Math-stub