# Does the dirac delta function have a Laplace transform?

1. Jan 5, 2012

### AdrianZ

If yes, how can we find it?

2. Jan 5, 2012

### LCKurtz

The δ function isn't actually a function; it is a distribution. It can be thought of informally as the limiting case of a pulse$$f(t) = \left \{\begin{array}{rl} h, & 0 < t < \frac 1 h\\ 0,& \frac 1 h < t \end{array}\right.$$ Then, again informally, you can calculate its LaPlace transform by working$$\lim_{h\rightarrow \infty}\int_0^{\frac 1 h} he^{-st}\, dt$$ You should get an answer of 1.

Last edited: Jan 5, 2012
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