Thanks for pointing that out, I have been doing more DSP lately (without sampling) and had somehow managed to confuse the real-time version of the delta with the discrete one ( delta(n) = { 1 if n = 0 { 0 otherwise )

After reading both of your explanations I realised that my working was incorrect as it was a weird hybrid.

Now that I have revised the correct continuous time version, I understand David's original working and also remember trying to do it the way Airy is doing it when I first learnt about laplace transforms. It wasn't fun lol.

Just to clarify to make sure im not off the rails again: Airy, I dont understand why you can't call f(t).delta(t-T) = g(t)? I personally cannot see anything wrong with it. g(t) itself will be undefined at T and zero at t = not T. But since it is being integrated, the sifting theorem should still work shouldn't it?

More importantly you should be able to go: g(t) = e^-(st).f(t) now you have: int(from 0 to inf) of ( g(t).delta(t-T) ) dt which is a basic sifting theorem problem which David illustrated previously.

Cheers Marc