\documentclass[12pt]{beamer}
\usepackage{pgfplots}
\usepackage{tikz}
\begin{document}
\begin{figure}%
\begin{tikzpicture}[scale=0.8]
\begin{axis}[axis lines=middle, xtick={-3,-2,...,5,9},
xticklabels={-3,{}, -1, 0, 1, {}, {}, {}, 5, $k$},
extra x ticks={-2, 2, 3, 4},
extra x tick labels={$-2$, $2$, $3$, $4$},
extra x tick style={
xticklabel style={yshift=0.5ex, anchor=south}},
xmin=-5,xmax=11, ytick={\empty}, yticklabels={},
ymin=-5, ymax=6, axis on top]
\addplot+[ycomb,black,thick] plot coordinates
{(-3,3) (-2,-2) (-1,1.5) (0,4) (1,1.5) (2,-1.5) (3, -3)
(4,-1) (5,4) (9,5)};
\end{axis}
\node at (5.1,3.5) {$\cdots$};
\node at (0,3.5) {$\cdots$};
\node at (0.8,4.5) {\tiny{$x[-3]\delta[n+3]$}};
\node at (2.7,4.8) {\tiny{$x[0]\delta[n]$}};
\node at (4.2,5) {\tiny{$x[5]\delta[n-5]$}};
\node at (6,5.5) {\tiny{$x[\alert{k}]\delta[n-\alert{k}]$}};
\node at (6.8,2.2) {$n$};
\node at (2.7,5.7) {$x[n]$};
\end{tikzpicture}
\end{figure}
\end{document}
After some more searching in this forum, I have come up with this code and the associated plot. The positioning of the things I want is a kludge.
Questions: All the positioning is manual (by trial and error). Even the x- and y-axis labels I had to locate by trial and error. Can this be automated? When I change the fontsize for the x-labels (e.g., \footnotesize), their alignmens get messed up.

