I am trying to create brown noise by integration of white noise (random walk).

I created Gaussian white noise. The histogram shows Gaussian distribution and Welch (and also FFT) shows flat spectrum.

Now I try to integrate it

$x(k+1) = x(k) + q(k)$

where $q$ stands for white noise and $x$ for resulting Brownian noise.

But the resulting spectrum isenter image description here

According Wikipedia I would expect that there should be straight line in the plot.

What I am doing wrong?

  • 1
    $\begingroup$ It looks like you are plotting the magnitude. Convert your amplitude scale to dB. $\endgroup$
    – Envidia
    May 11, 2017 at 17:32
  • $\begingroup$ @Envidia Do you mean frequency scale? If yes, then you are right! It should be log-log, not semilog. $\endgroup$
    – matousc
    May 11, 2017 at 17:44
  • $\begingroup$ I'm referring to the vertical scale. Is that in dB? Also, some code would be good to see. $\endgroup$
    – Envidia
    May 11, 2017 at 17:49
  • $\begingroup$ @Envidia The vertical scale is ok. If I make the horizontal scale also logarithmic, I can get the line (decreasing 1 decade per decade). What is corresponding to 20db per decade as is shown here en.wikipedia.org/wiki/Brownian_noise#/media/… $\endgroup$
    – matousc
    May 11, 2017 at 17:53
  • $\begingroup$ You got it. I stubbornly assumed your scale was correct. $\endgroup$
    – Envidia
    May 11, 2017 at 18:09

1 Answer 1


So this question does not remain as unanswered:

Making your horizontal scale into log-scale should give you the decade drop and yield the linear amplitude graph.


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