DescriptionColored noise.png	English: Example of noise signals with different power spectra.
Date	16 July 2019
Source	https://twitter.com/j_bertolotti/status/1151129795008200707
Author	Jacopo Bertolotti
Permission (Reusing this file)	https://twitter.com/j_bertolotti/status/1030470604418428929
Other versions	This file has an extracted image: Colored noise (cropped).png.

n = 4096;
\[Phi] = RandomReal[{0, 2 \[Pi]}, n];
\[Epsilon][i_, \[Alpha]_] := Sum[Sqrt[k^-\[Alpha] Abs[(2 \[Pi])/n]^(1 - \[Alpha])]*Cos[(2 \[Pi] i k)/n + \[Phi][[k]]], {k, 1, n/2}];
red = Table[\[Epsilon][i, 2.], {i, 1, n}];
white = Table[\[Epsilon][i, 0.], {i, 1, n}];
pink = Table[\[Epsilon][i, 1.], {i, 1, n}];
blue = Table[\[Epsilon][i, -1.], {i, 1, n}];
GraphicsGrid[{{
ListPlot[blue, Joined -> True, PlotStyle -> LightBlue, LabelStyle -> {LightBlue, Bold}, AxesLabel -> {"t", ""}, Ticks -> None, Axes -> {True, False}, PlotLabel -> "Blue noise"],
ListLogLogPlot[Evaluate[(Abs[Fourier[blue]]^2)[[2 ;; n/2]]], Joined -> True, PlotRange -> All, PlotStyle -> {LightBlue, Thick}, Axes -> False, Frame -> True, FrameLabel -> {"\[Omega]", "Power spectrum"}, LabelStyle -> {LightBlue, Bold}, GridLines -> Automatic]
    }, {
ListPlot[white, Joined -> True, PlotStyle -> White, LabelStyle -> {White, Bold}, AxesLabel -> {"t", ""}, Ticks -> None, Axes -> {True, False}, PlotLabel -> "White noise"], ListLogLogPlot[Evaluate[(Abs[Fourier[white]]^2)[[2 ;; n/2]]], Joined -> True, PlotRange -> All, PlotStyle -> {White, Thick}, Axes -> False, Frame -> True, FrameLabel -> {"\[Omega]", "Power spectrum"}, 
LabelStyle -> {White, Bold}, GridLines -> Automatic]
    }, {
ListPlot[pink, Joined -> True, PlotStyle -> Pink, LabelStyle -> {Pink, Bold}, AxesLabel -> {"t", ""}, Ticks -> None, Axes -> {True, False}, PlotLabel -> "Pink Noise"], ListLogLogPlot[Evaluate[(Abs[Fourier[pink]]^2)[[2 ;; n/2]]], Joined -> True, PlotRange -> All, PlotStyle -> {Pink, Thick}, Axes -> False, Frame -> True, FrameLabel -> {"\[Omega]", "Power spectrum"}, 
LabelStyle -> {Pink, Bold}, GridLines -> Automatic]
    }, {
ListPlot[red, Joined -> True, PlotStyle -> Red, LabelStyle -> {Pink, Bold}, AxesLabel -> {"t", ""}, Ticks -> None, Axes -> {True, False}, PlotLabel -> "Red Noise"],
ListLogLogPlot[Evaluate[(Abs[Fourier[red]]^2)[[2 ;; n/2]]], Joined -> True, PlotRange -> All, PlotStyle -> {Red, Thick}, Axes -> False, Frame -> True, FrameLabel -> {"\[Omega]", "Power spectrum"}, 
    LabelStyle -> {Red, Bold}, GridLines -> Automatic]
    }}, ImageSize -> Large, Background -> Black]

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