# Creation of Brownian noise as random walk

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 is

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

What I am doing wrong?

• It looks like you are plotting the magnitude. Convert your amplitude scale to dB. – Envidia May 11 '17 at 17:32
• @Envidia Do you mean frequency scale? If yes, then you are right! It should be log-log, not semilog. – matousc May 11 '17 at 17:44
• I'm referring to the vertical scale. Is that in dB? Also, some code would be good to see. – Envidia May 11 '17 at 17:49
• @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/… – matousc May 11 '17 at 17:53
• You got it. I stubbornly assumed your scale was correct. – Envidia May 11 '17 at 18:09