Dirac Delta Function
vanishes away from , has unit integral, and samples continuous : .
Definition 6.22 (Dirac Delta Function)
The Dirac delta function is defined by
It is technically not a function, but a distribution. It only makes sense under an integral.
Properties
The Dirac delta function has the following properties:
-
for all .
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.
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(Sampling property.) For all functions that are continuous at ,
More generally, for a function continuous at ,
Related
Stated in
- Definition 6.22 (Dirac Delta Function)§6.8.1 Dirac Delta Function