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Signals and Systems by Smarajit Ghosh

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4.7 LAPLACE TRANSFORM OF SOME COMMON TIME FUNCTION

4.7.1 Unit Step Function

It is the most common driving function in electrical engineering and is denoted by

 

image

 

∴ The Laplace transformation of unit step function can be written as

 

image

 

The both terms within the bracket are oscillating functions and hence can not be zero for t image . Therefore, for convergence e σt 0 at t = when σ > 0.

Figure 4.1 shows the region of convergence.

 

 

Fig. 4.1 ...

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