digital-brain/content/zettels/laplace_transform.md

+++ title = "Laplace Transform" author = ["Dehaeze Thomas"] draft = false +++

Tags

[Continuous Transfer Functions]({{< relref "continuous_transfer_functions.md" >}})

Definition

Laplace transform:

\begin{equation} \boxed{F(s) = \mathcal{L}{f(t)} = \int_0^\infty e^{-st} f(t) dt} \end{equation}

Laplace transform of signals

https://en.wikipedia.org/wiki/List_of_Laplace_transforms

Laplace transform of functions

https://en.wikibooks.org/wiki/Signals_and_Systems/Table_of_Laplace_Transforms

Solving Linear Differential equations

Mechanical System

Electrical System