- #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. In fact 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