# Definition of the Dirac Delta Distribution

$ \delta(t) = \lim_{\epsilon\rightarrow0} \frac{1}{\epsilon}\left[u(t+\epsilon/2) - u(t-\epsilon/2)\right], $

where $ u(t) = 0 $ for $ t<0 $ and $ u(t)=1 $ for $ t\geq0 $

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