(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Prove that

[tex]\displaystyle \int_{-\infty}^{\infty} \delta (at - t_0) \ dt = \frac{1}{ | a |} \int_{-\infty}^{\infty} \delta (t - \frac{t_0}{a}) \ dt[/tex]

For some constant a.

3. The attempt at a solution

Edit: Looking at this again, I really don't understand where this is coming from. Everywhere I've read has just said to do a change of variable with u = at, but performing this change of variable, I get

[tex] \displaystyle \frac{1}{a} \int_{-\infty}^{\infty} \delta (u - t_0) \ du [/tex]

I don't really understand where the absolute value or the [tex]t_0 / a[/tex] come from.

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# Scaling Property of the Dirac Delta Function

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