Signals and Systems

4.8 LAPLACE TRANSFORM OF TWO-SIDED FUNCTIONS (BLT)

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.

4.8.1 ROC for f(t) = e^btu(−t)

Let us consider a function f (t) = e^btu(–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) = e^btu(–t)

 

The Laplace transform of this function is given by

 

 

 

will be zero if and only if σ < b.

 

 

where ...