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I saw the above tutorial by arildno and looked at how he defined the Dirac Delta "function" as a functional. But isn't there a more easier way to do this. I have seen the following definition in a lot of textbooks.

[tex]\delta(t) \triangleq \lim_{\epsilon \to 0} \frac{1}{\epsilon} \Pi\Big(\frac{t}{\epsilon}\Big)[/tex]

where [tex]\Pi(t)[/tex] is the gate function and is defined as

[tex]

\Pi (t) :=

\begin{cases}

0 & \mbox{ for } |x| > \frac{1}{2} \\

\frac{1}{2} & \mbox{ for } |x| = \frac{1}{2} \\

1 & \mbox{ for } |x| < \frac{1}{2},

\end{cases}

[/tex]

What's wrong by defining the delta function in this way?

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# Defining Dirac Delta Function

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