\documentclass{standalone}

\usepackage{tikz}
\usepackage{pgfplots}
\usepgfplotslibrary{colorbrewer}
\pgfplotsset{compat=1.11}

\pgfplotsset{grid style={dotted, gray!80!white}}

\begin{document}
  \begin{tikzpicture}[>=latex]
    \begin{axis}[domain=0:2, samples=512, hide x axis, hide y axis,
      xlabel={Time}, ylabel={Amplitude},
      cycle multi list={Set1-4}, xmin=0, xmax=2, ymin=-15, ymax = 1,
      minor x tick num={1}]
      \addplot+[no marks, smooth, thick] {sin(deg(2*pi*10*x)) - 6};
      \addplot+[no marks, smooth, thick] {sin(deg(2*pi*20*x))};
      \addplot+[no marks, smooth, thick] {sin(deg(2*pi*15*x)) - 3};
      
      \node at (axis cs:1.5, -1.5) {$+$};
      \node at (axis cs:1.5, -4.5) {$+$};
      \node at (axis cs:1.5, -7.5) {$+$};
      \node at (axis cs:1.5, -8.5) {$\vdots$};
      \node at (axis cs:1.5, -10) {$=$};

      \addplot[no marks, smooth, thick] {sin(deg(2*pi*12*x))*exp(-(x-1)^2/(2*0.25^2)) - 11.5};

      \node (source) at (axis cs:0.5, -13.2) {};
      \node (dest) at (axis cs:1.5, -13.2) {};
      \draw[<->] (source)--(dest) node [midway, fill=white] {$\tau_c$};
      \draw[dashed, gray!85!white] (axis cs:1, -12.5) -- (axis cs:1, 1);
      %\draw[dotted] (source) -- (axis cs:0.5, -11.5);
      %\draw[dotted] (dest) -- (axis cs:1.5, -11.5);
    \end{axis}
  \end{tikzpicture}
\end{document}