## u(t)*DiracDelta[t]=u(t)? [closed]

can someone tell me if that's a true statement for LTI systems: u(t)*DiracDelta[t]=u(t)

if you can add a proof i'll be thankful.

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What's an LTI system? Is the * in your formula convolution? Is u the heaviside function? Actually, the most important of these is the second since the dirac delta function is the unit for convolution. The proof can be found in any rigorous treatment of Fourier systems that mentions distributions. – Andrew Stacey May 11 2010 at 6:27
As Andrew has said: you haven't defined the terms in your question in adequate detail; and moreover I think your question is answered in any of the standard sources for Fourier transforms of distributions, or heuristically covered in texts on Fourier/Laplace transforms. – Yemon Choi May 11 2010 at 9:59
Moreover, I don't think this question really fits into MO's approximate remit of "questions of interest to research mathematicians"... – Yemon Choi May 11 2010 at 9:59
@Andrew: I'll bet that LTI stands for “linear and translation invarian”. – Harald Hanche-Olsen May 11 2010 at 11:12