This isn't really homework, I'm just curious. So I'm dealing with the delta dirac function, and I was just wondering what would happen if we had two functions.(adsbygoogle = window.adsbygoogle || []).push({});

So the sampling property,

[tex] \int_{-\infty}^{\infty} f(t)\delta(t-a)\,\,dt = f(a) [/tex]

Now what if we had:

[tex] \int_{-\infty}^{\infty} f(t)\delta(t-a)\delta(t-b)\,\,dt =?[/tex]

What would happen?

My guess would be the following:

If [itex] a = b [/itex]:

[tex] \int_{-\infty}^{\infty} f(t)\delta(t-a)\delta(t-b)\,\,dt =\int_{-\infty}^{\infty} f(t)\delta(a)\,\,dt =\int_{-\infty}^{\infty} f(t)\delta(b)\,\,dt [/tex]

If [itex] a \neq b [/itex]:

[tex] \int_{-\infty}^{\infty} f(t)\delta(t-a)\delta(t-b)\,\,dt = 0 [/tex]

Or is my answer or question just nonsense?

-Thanks

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# Homework Help: Delta Function

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