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 .

i.e, .

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.

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