Symbol for Laplace Transform : 2 connected dots, one filled

Question

What I want is the following:

x(t) ●-o \hat{x}(f) (The bar should be longer)

What is the name of the symbol in between and does it exist in LaTeX?

Answer 1

A closer look through the Comprehensive LaTeX Symbol List also reveals the following aditional examples:

\documentclass{article}

\usepackage{txfonts}

\begin{document}

\begin{equation}
x(t) \multimapdotbothB \hat{x}(f)     
\end{equation}

\end{document}

\documentclass{article}
\usepackage{stix}

\begin{document}

\begin{equation}
x(t) \imageof \hat{x}(f)
\end{equation}

\end{document}

\documentclass{article}
\usepackage{fdsymbol}
\begin{document}

\begin{equation}
x(t) \blackwhitespoon \hat{x}(f)
\end{equation}

\end{document}

Answer 2

The trsym and the trfsigns packages both have this symbol (whose name, however, is not known to me). The symbol from the trfsigns package is somewhat longer but would perhaps benefit from some additional spacing.

\documentclass{article}
\usepackage{trsym,trfsigns}

\begin{document}

\begin{equation}
x(t) \InversTransformHoriz \hat{x}(f)  % trsym package
\end{equation}

\begin{equation}
x(t) \Laplace \hat{x}(f)               % trfsigns package
\end{equation}

\end{document}

Additionally, the txfonts/pxfonts and the boisik packages have \multimapdotbothB, which you could also use. However, the txfonts/pxfonts package will change the default font and the boisik package needs some additional set up when used with XeLaTeX.