# Does the dirac delta function have a Laplace transform?

1. Jan 5, 2012

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.