I found this interesting little problem when thinking about convolution:(adsbygoogle = window.adsbygoogle || []).push({});

[tex] \int x( \tau) \delta(t-\tau) d\tau [/tex]

Normally to solve something like this you would have to integrate by parts because of two functions in [tex]\tau[/tex]

Using the fact that:

[tex] \int u *dv = u*v - \int v*du [/tex]

Where

[tex] u=x(\tau)[/tex]

[tex] dv= \delta(t-\tau) d\tau[/tex]

Then:

[tex] du=x'(\tau) d\tau[/tex]

[tex] v= 1 [/tex]

If you plug this back in you get:

[tex]x(\tau) - x(\tau) = 0[/tex]

Total nonsense!

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# Integrate by parts because of two functions

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