Hilbert Transform in LaTeX equation

Question

I'm having a bit of trouble representing the following equation.

Some attempts I've made are below.

\begin{tabular}{c}
\centering
$x \Rightarrow \hat{x}$ \\ 
$\hat{z} = 
 \begin{cases}
 \hat{x} \times 2 & \text{if} x > 0\\
 0 & \text{if} x < 0 
 \end{cases}$ \\ 
$\hat{z} \Rightarrow z $ 
\end{tabular} 

Another unsuccessful option:

\begin{eqnarray}
x \Rightarrow \hat{x} \nonumber\\
\hat{z} = \begin{cases} \hat{x} \times 2 & \text{if} x > 0\\0 & \text{if} x 
 < 0\end{cases} \nonumber \\
\hat{z} \Rightarrow z \nonumber
\end{eqnarray}

Suggestions welcome.

Answer 1

The various align environments from the amsmath package are the most useful for aligning math content along one or more alignment points. Centering of math is most easily achieved by invoking display math via \[...\].

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\[
\begin{aligned}
x &\Rightarrow \hat{x} \\ 
\hat{z} &= 
 \begin{cases}
 \hat{x} \times 2 & \text{if } x > 0\\
 0 & \text{if } x < 0 
 \end{cases} \\ 
\hat{z} &\Rightarrow z  
\end{aligned}
\]
\end{document}