- #1

thomas49th

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## Homework Statement

The Dirac function (unit impulse) is defined as

[tex]\delta(t) = 0[/tex] where [tex]t \neq 0[/tex]

the integration of d(t) between -ve inf and +ve inf is 1.

Now I picture this as a rectangle with no width and infinite height. Infact I think of the width (along the x axis) as (1/inf = 0) and the height being inf. So the area (integral) is 1/inf * inf = 1

However if the width is 0, then why does the integral have limits between -inf and +inf?

Am I right in the thinking when a signal g(t) is multiplied by the Dirac function it just turns a signal "on" for an infintately small amount of time?

Can someone please explain how

[tex] \int_{-\infty}^{\infty} \delta(t-T)g(t)dt = g(T)[/tex]

I am having problems relating this to the real world

Thanks

Thomas