Drawing and inserting mathematical symbols on a Dia generated graph

Final

\documentclass[pstricks,border=12pt,12pt]{standalone}
\usepackage{amsmath}
\usepackage{pst-plot,pst-node}
\psset{algebraic,plotpoints=100,labelsep=3pt}

\def\f[#1,#2]{2*2^(-2.5*(#1-#2)^2)}

\begin{document}
\begin{pspicture}[showgrid=false](-3,0)(3.5,3)
    \psaxes[axesstyle=frame,tickstyle=bottom,ticks=x,ticksize=0 4pt,xsubticks=5,xsubticksize=.5,labels=none](0,0)(-3,0)(3,3)
    \uput[d](-1,0){$\omega_{\text{nl}}$}
    \uput[d](1.5,0){$\omega_{\text{lin}}$}
    \uput[d](0,0){\tiny Frequency}
    \psline{<-}(0,2)(1,2)
    \psset{linecolor=gray}
    \psline[linestyle=dashed](0,0)(0,3) 
    \psplot[linecolor=red,linestyle=dashed]{-3}{1}{\f[x,-1]}
    \psplot[linecolor=red]{-.5}{3}{\f[x,1.5]}
    \pcline{<->}(*-1.5 {\f[x,-1]})(*-.5 {\f[x,-1]})\nbput{$r_{\text{nl}}$}
    \pcline{<->}(*1 {\f[x,1.5]})(*2 {\f[x,1.5]})\nbput{$r_{\text{lin}}$}
\end{pspicture}
\end{document}

If you have the complete drawing in Dia, you can chose to export the picture as LaTeX PGF macros. You'll then have a .tex file, lets say yourDiaDrawing.tex, which you can include in your document by \input{pathToFile/yourDiaDrawing.tex}. If you have added your labels in Dia, find the nodes containing your label texts in yourDiaDrawing.tex. When exporting to TikZ, Dia assumes that every special character you have inserted are supposed to be that way, and escapes the characters. So your math dollars will be escaped \$, your backslashes will be escaped \\ and so on. Remove the backslash, and LaTeX does the rest.

You'll probably find nodes in yourDiaDrawing.tex that'll look something like this

\node[anchor=west] at (13.00\du,8.00\du){\$ \\alpha \$};

There is a patch to keep TeX formulae unescaped in PGF export. Hopefuly, it will be merged soon.

See https://bugzilla.gnome.org/show_bug.cgi?id=778836 and https://gitlab.gnome.org/GNOME/dia/merge_requests/3