# s-plane

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.
${\displaystyle \int _{0}^{\infty }f(t)e^{-st}\,dt\;|\;s\;\in \mathbb {C} }$