# Noisy, analogue waveform in TikZ

Is there an easy way of drawing a noisy waveform in TikZ? I know you can draw a simple sinusoid by repeatedly using cos and sin for every half-period, but doing that for a noisy waveform seems like a massive undertaking and a very roundabout way of doing it.

I'm looking for something like this:

It doesn't have to be that long, a fifth of the length is fine. I'm diagramming a noise reduction system and need to show a noisy waveform as the input to the diagram (whereas the rest of the diagram is simple rectangular boxes and text...).

Any ideas?

• Commented Nov 10, 2013 at 20:47
• Thanks for that. I just discovered TikZ today and it's surprisingly powerful! Commented Nov 10, 2013 at 21:30

You can use \draw plot for plotting functions. For the noise, you can use the rand function.

In general, plotting is more comfortable using the PGFPlots package, which builds on PGF/TikZ:

\documentclass{article}
\usepackage{pgfplots}
\begin{document}
\begin{tikzpicture}[samples=200, domain=0:5*360]
\begin{axis}[
width=10cm, height=4cm,
enlarge x limits=false,
xtick=\empty,
axis lines*=middle,
hide y axis
]
\end{axis}
\end{tikzpicture}
\end{document}

• why sin(x) and not only rand? Commented Dec 13, 2015 at 21:13
• I just think it's a prettier function than pure noise. No technical reason though (but jodles did ask for a "noisy waveform" and not "pure noise", so I guess it's closer to what they were looking for)
– Jake
Commented Dec 13, 2015 at 21:19
• OK. I need white noise and I am using something like +rand-rand+rand-rand to make it as random as possible. Commented Dec 13, 2015 at 21:21
• @Pygmalion: I don't think that actually increases the randomness. It does change the distribution of your values, though, which might be undesirable: see stackoverflow.com/a/3956538/1456857
– Jake
Commented Dec 13, 2015 at 21:38
• @Jake Thanks for the stackoverflow.com/questions/3956478 hint! Commented Aug 14, 2017 at 19:53

This is a derived example from the »PGF/TikZ« user guide.

\documentclass{article}
\usepackage{tikz}

\begin{document}
\begin{tikzpicture}[
declare function={
excitation(\t,\w) = sin(\t*\w);
noise = rnd - 0.5;
source(\t) = excitation(\t,20) + noise;
filter(\t) = 1 - abs(sin(mod(\t, 50)));
speech(\t) = 1 + source(\t)*filter(\t);
}
]
\draw[help lines] (0,1) -- (3,1);
\draw[blue, thick, x=0.0085cm, y=1cm] (0,1) -- plot [domain=0:360, samples=144, smooth] (\x,{speech(\x)});
\end{tikzpicture}
\end{document}


Customization is left to you.

With PSTricks.

\documentclass[pstricks,border=12pt]{standalone}
\usepackage{pst-plot,pst-node}
\psset{plotpoints=200,linejoin=1}
\pstVerb{realtime srand}

\begin{document}
\psLoop{10}{%
\begin{pspicture}[showgrid=false](-4,-2)(4.5,2.5)
\psaxes[labels=none,ticks=none,linecolor=gray]{->}(0,0)(-4,-2)(4,2)[$t$,0][$v$,90]
\psplot[linecolor=red]{-3.8}{3.8}{x 5 mul RadtoDeg sin Rand 4 mul 1 sub mul 1.8 mul}
\end{pspicture}}
\end{document}


## Attention

Note that Rand no longer produces a random real number between 0 and 0.5 inclusive. Its definition had been tacitly changed. Now it produces a random real number between 0 and 1 inclusive. It is not documented, nor announced, but it is still fun!

The code given above has not been updated yet so it will produce different output. I have no time to update it right now. Sorry for this inconvenience.

• A plot continuously moving from right to left would be even cooler. Commented Nov 11, 2013 at 7:51
• @AlexG: Yes. I will see it later. Commented Nov 11, 2013 at 8:22
• This is not working :(
– Bob
Commented Nov 29, 2017 at 15:52

If you want just the noise part without any sinusoidal excitation, you can customize the Donig's code by just removing the sinusoidal excitation. In addition, you can shift the noise location by just adding the xshift and yshift commands, as

\documentclass{standalone}
\usepackage{tikz}
\usepackage{pgfplots}
\begin{document}
\begin{tikzpicture}[
declare function={
noise = rnd - 0.1;
speech(\t) = noise;
}
]
\draw[help lines] (0,1) -- (1,1);
\draw[blue, thick, x=0.0415cm, y=1.15cm, yshift=-6cm] (0,1) -- plot [domain=0:360, samples=1044, smooth] (\x,{speech(\x)});
\end{tikzpicture}
\end{document}


• is it possible to let the noise originate from a \node? when i say originate from (nodea.east) it does not work Commented Mar 9, 2023 at 10:32
• When using a node coordinate like (node.east) as the seed for the random number generator, you need to make sure that the coordinates are converted to a number using \pgfmathparse and \pgfmathresult, since the \pgfmathsetseed command expects a number as its argument. To generate the noise function from a node, you can use the \pgfmathsetseed command to set the random number generator seed based on the coordinates of the node. Commented Mar 11, 2023 at 5:07