The Laplace transform is defined as below :

Let f(t) be a real function of a real variable t defined for t˃0, then

Where F(s) is called Laplace transform of f(t). and the variable 's' which appears F(s) is frequency dependent complex variable. It is given by,

Where σ = Real part of complex variable 's'.

ω= Imaginary part of complex variable 's'.

The time function f(t) is obtained back from the Laplace transform by a process called Inverse Laplace transform and denoted as L

^{-1}. Thus,
The time function f(t) and its Laplace transform F(s) is called transform pair.

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