\documentclass[12pt]{article}
\begin{document}
\setlength{\unitlength}{1.5cm}
\begin{figure}
\begin{center}
\begin{picture}(6,4)(-3,-2)
\put(-2.5,0){\vector(1,0){5}}
\put(0,-1){\vector(0,1){3}}
\multiput(-2.5,1)(0.4,0){13}
  {\line(1,0){0.15}}
\qbezier(0,0)(0.25,0.01)(0.5,0.5)
\qbezier(0.5,0.5)(0.75,0.99)(1,1)
\put(1,1){\line(1,0){1.5}}
\put(-2.5,0){\line(1,0){2.5}}
\put(-0.256,0.965){$s$}
\put(-0.256,1.9){$y$}
\put(2.4,0.1){$\tau$}
\put(0.75,0.5){$y=\rho(\tau)$}
\multiput(-3,-1.75)(6,0){2}{\line(0,1){4.}}
\multiput(-3,-1.75)(0,4.){2}{\line(1,0){6}}
\end{picture}
\caption{A step function}
\end{center}
\end{figure}
\end{document}