Let us discuss about the Laplace transform of two-sided function. Let us first consider a negative function and then a positive function. Then we will consider the two-sided function.
Let us consider a function f (t) = ebtu(–t) which has been shown in Fig. 4.6. This a negative function of time and b is a positive quantity.
Fig. 4.6 f (t) = ebtu(–t)
The Laplace transform of this function is given by
will be zero if and only if σ < b.