+inf +inf

Sum d(t - n

***T) is 2***Pi/T Sum d(s/j - 2*Pi/T)

-inf -inf

I unsuccessfully tried to find the steps between the function and its

transform via two paths.

First, since the Dirac's comb is an infinite sequence of Dirac's

impulses, some advanced before t=0, and others delayed after t=0, the

delay theorem comes to the mind. Moreover, the Laplace Transform of

the Dirac's impulse being 1, it could not be simpler!

... + exp(-2

***s***T) + exp(-2

***s***T) + exp(0

***s***T) + exp(1

***s***T) +

exp(2

***s***T) + ...

Oops! This series does not converge in the normal sense. It should

converge in the sense of distributions, but I do not know how to

handle it. :-(

Second, I start from the definition of the Laplace Transform.

+inf +inf

Integral Sum d(t - n

***T) exp(-s***t) dt

-inf -inf

I change the order of the sum and the integral.

+inf +inf

Sum Integral d(t - n

***T) exp(-s***t) dt

-inf -inf

Since the Dirac's impulse differs from 0 only when t=n

***T and has an**

«area» of 1, I can drop the integration.

+inf

Sum exp(-s*t) dt

«area» of 1, I can drop the integration.

+inf

Sum exp(-s*

-inf

Alas! I fall in the same dead-end as I fell above!

Could you help me find the way?

Thank you very much in advance.