The Fourier transform of a signal x(t) is given as
Fourier Transform exists only if
we know that
if we compare Equations (I) and (II) both are equal when .
This means that Laplace Transform is same as Fourier transform when .
Fourier Transform is nothing but the special case of Laplace transform where indicates the imaginary axis in complex-s-plane.
Thus Laplace transform is basically Fourier Transform on imaginary axis in the s-plane.