I have recently digged up a post in the forum about a confusion arise from definition of Dirac Delta function and I am actually really bothered by it (link to the thread).(adsbygoogle = window.adsbygoogle || []).push({});

When people talk about sampling some function f(x) with Dirac Comb, or impulse train, they would be talking about the product of f(x) and the Dirac Comb:

$$f'(x)=\sum_{n=-\infty}^{\infty}f(x)\cdot\delta(x-nT)$$

And as we all know δ(0)=infinite instead of 1, this doesn't make sense to me since III(x) would be a train of infinite instead of 1.

However, Wikipedia and some text books about Signal Processing almost always leave out the integration as in the definition of Dirac Delta:

$$f(X)=\int^\infty_{-\infty}\delta(x-X)\cdot f(x)dx$$

I understand that Dirac Delta is not well defined in mathematics, but when I think deeply, I don't see the why Dirac Delta have to be infinite at x=0. Why Dirac use +infinite instead of 1 or any other values? And can it really sample a function without the integration?

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# Dirac Delta Comb confusions

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