Noisy, analogue waveform in TikZ

Question

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: Noisy waveform

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?

Related: Plotting a random function f(x) and f(x)+sin(x) with tikz — Qrrbrbirlbel, Nov 10 '13 at 20:47
Thanks for that. I just discovered TikZ today and it's surprisingly powerful! — jodles, Nov 10 '13 at 21:30

score 29 · Accepted Answer · answered Nov 10 '13 at 18:51

29

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
        ]
        \addplot [no markers, smooth] {sin(x)+rand*2};
        \end{axis}
    \end{tikzpicture}
\end{document}

answered Nov 10 '13 at 18:51

Jake

232,450

why sin(x) and not only rand? – Pygmalion Dec 13 '15 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 Dec 13 '15 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. – Pygmalion Dec 13 '15 at 21:21
3

@Pygmalion: I don't think that actually increases the randomness. It does change the distribution of your values, though, which might be undesirable: see http://stackoverflow.com/a/3956538/1456857 – Jake Dec 13 '15 at 21:38
@Jake Thanks for the https://stackoverflow.com/questions/3956478 hint! – Dr. Manuel Kuehner Aug 14 '17 at 19:53

kiss my armpit · Answer 2 · 2013-12-26T08:12:00.037

12

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}

enter image description here

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.

edited Dec 26 '13 at 08:12

answered Nov 10 '13 at 18:54

kiss my armpit

36,086

1

A plot continuously moving from right to left would be even cooler. – AlexG Nov 11 '13 at 07:51
@AlexG: Yes. I will see it later. – kiss my armpit Nov 11 '13 at 08:22
This is not working :( – Bob Nov 29 '17 at 15:52

score 12 · Answer 3 · answered Nov 10 '13 at 18:56

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.

enter image description here

score 1 · Answer 4 · answered May 06 '17 at 09:07

1

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}

answered May 06 '17 at 09:07

Pankaj Singh

107
3

is it possible to let the noise originate from a \node? when i say originate from (nodea.east) it does not work – intStdu Mar 09 '23 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.
– Pankaj Singh Mar 11 '23 at 05:07

Noisy, analogue waveform in TikZ

4 Answers4

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