S-plane

In mathematics and engineering, the s-plane is the complex plane on which Laplace transforms are graphed. It is a mathematical domain where, instead of viewing processes in the time domain modelled with time-based functions, they are viewed as equations in the frequency domain. It is used as a graphical analysis tool in engineering and physics.

A real function (f) in time 't' is translated into the s-plane by taking the integral of the function multiplied by ${\displaystyle e^{-st}}$ from ${\displaystyle 0}$ to ${\displaystyle \infty }$ where s is a complex number with the form ${\displaystyle s=\sigma +j\omega }$. Coordinates in the s-plane use 'j' to designate the imaginary component, in order to distinguish it from the 'i' used in the normal complex plane.

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