A sine curve, where the y-values do not exceed a certain value.

PGFPlots has two different types of clipping: the first is the graphical clipping operation which is activated by clip, the second is based on coordinate value manipulation, more precisely by restrict y to domain*.

\documentclass[border=10pt]{standalone}\usepackage{pgfplots}\pgfplotsset{width=7cm,compat=1.8}% Create a function for generating inverse normally distributed numbers using the Box–Muller transform\pgfmathdeclarefunction{invgauss}{2}{%\pgfmathparse{sqrt(-2*ln(#1))*cos(deg(2*pi*#2))}%}\newcommand*{\val}{0.8}% the absolut value of the limit% Code for brownian motion\begin{document}\begin{tikzpicture}\begin{axis}[
domain = -6.283:6.283,
grid = both, minor tick num=2,
title = Clipped Output Sine Wave Signal,
xlabel = Time,
ylabel = Volt,
legend pos = outer north east,
restrict y to domain* = -\val:\val]\addplot[blue, line width=2pt]{\val};
\addplot[blue!50, line width=2pt]{-\val};
\addplot+[no marks, samples=100, red, line width=2pt]{sin(deg(x))};
\legend{max.Output Voltage, max.Output Voltage, Clipped Signal}\end{axis}\end{tikzpicture}\end{document}