If the Laplace Transform of
'x(t)' is 'X(s)' , then the Inverse Laplace Transform of
X(s) is given by
where 'C' is any vertical line in the s plane, that is, parallel to the imaginary axis.
Fourier Transform of 'x(t)' = Laplace Transform of
'x(t)' when s=jw i.e. if the imaginary axis lies in the Region of Convergence of
'X(s)' and the Laplace Transform is evaluated along it , then the result is the Fourier Transform of
'x(t)'.
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