S-plane

In mathematics, the Laplace transform, named after Pierre-Simon Laplace (), is an integral transform that converts a function of a realvariable (usually ⁠${\displaystyle t}$⁠, in the time domain) to a function of a complex variable${\displaystyle s}$ (in the complex-valued frequency domain, also known as s-domain or s-plane). The functions are often denoted using a lowercase symbol for the time-domain function and the corresponding uppercase symbol for the frequency-domain function, e.g. ${\displaystyle x(t)}$ and ⁠${\displaystyle X(s)}$⁠.