X-Nico

7 unusual facts about Dirac delta function


Dirac delta function

Namely, such a null sequence becomes an infinitesimal in Cauchy's and Lazare Carnot's terminology.

Dirac measure

The name is a back-formation from the Dirac delta function, considered as a Schwartz distribution, for example on the real line; measures can be taken to be a special kind of distribution.

Discrete measure

The simplest example of a discrete measure on the real line is the Dirac delta function \delta.

Green's function for the three-variable Laplace equation

and the point source is given by \delta(\mathbf{x}-\mathbf{x'}), the Dirac delta function.

Nyquist ISI criterion

We multiply such a h(t) by a sum of Dirac delta function (impulses) \delta (t) separated by intervals Ts This is equivalent of sampling the response as above but using a continuous time expression.

In practice this criterion is applied to baseband filtering by regarding the symbol sequence as weighted impulses (Dirac delta function).

Peakon

the second derivative uxx must be taken in the sense of distributions and will contain a Dirac delta function;


Time constant

In the time domain, the usual choice to explore the time response is through the step response to a step input, or the impulse response to a Dirac delta function input.


see also