Editing Analog signal processing (section)

===Laplace transform===
{{further|Laplace transform}}

The [[Laplace transform]] is a generalized [[Fourier transform]].  It allows a transform of any system or signal because it is a transform into the complex plane instead of just the jω line like the Fourier transform.  The major difference is that the Laplace transform has a region of convergence for which the transform is valid.  This implies that a signal in frequency may have more than one signal in time; the correct time signal for the transform is determined by the [[region of convergence]].  If the region of convergence includes the jω axis, jω can be substituted into the Laplace transform for s and it's the same as the Fourier transform.  The Laplace transform is:
:<math>X(s) = \int^\infty_{0^-} x(t)e^{-s t}\, dt</math>
and the inverse Laplace transform, if all the singularities of X(s) are in the left half of the complex plane, is:
:<math>x(t)=\frac{1}{2\pi}\int^\infty_{-\infty} X(s )e^{s t}\, d s </math>