Re: help with dirac delta function ?

On 2007-12-22 08:01:08 -0500, pagcal <pagcal@xxxxxxxxxx> said:

Can someone offer help understanding properties of the dirac delta function?

given

integ(delta(alpha*x)) = integ(delta(u)du/|alpha|) = 1/|alpha|

In the second term, how did magnitude alpha appear and in the
denominator?

integ is integral +infinity to -infin

You can also use the Fourier transform's property (scaling) that says
u(ax) =F.T.=> 1/|a| U(w/a)
where F.T.[u] = U.

Since F.T.[delta] = 1, therefore
delta(ax) = 1/|a| delta(x).

--

-kira

.

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