# Why is distorted / quantized white noise still white noise?

White noise can be created by setting every sample in the time domain to a random number with a gaussian distribution. Every sample is random, so the frequency response is obviously random. Easy enough.

Next step: Set every sample to a random number between 0 and 1, but the numbers are equally distributed instead of using a gaussian distribution (please ignore the DC offsets, they don't really matter). Samples are random enough, so it still makes sense that it would sound like white noise.

Now, set every sample to either 0 or 1 with a 50/50 chance. This feels like it shouldn't sound like white noise anymore, but it still does.

Finally, set every sample to either 0 or 1 with a 90/10 chance. How does this still sound like white noise when it looks nothing like it?

EDIT
I did some experimenting (with sample rate 48000 Hz).
1/2 chance is basically white noise.
1/4 chance sounds almost like white noise, but if you know what you're looking for it's easy to tell the difference.
1/16 chance sounds like rain smattering against something (you can hear individual impulses), with white noise in the background.

Varying the amplitudes of the impulses did not seem to have any effect on the sound, other than volume.

• To clarify: Gaussian distribution is not required to be "white". White refers to the uniform distribution in frequency and that every sample is independent/uncorrelated to the other samples. Gaussian refers to the distribution in magnitude which may or may not be for a white noise process. If you take the requirement or need to be "Gaussian" out of this, I think it will clear up your question. Sep 29, 2018 at 13:58
• @DanBoschen The first sentence I wrote wasn't supposed to frame gaussian as a requirement. It's more that I know that random samples with a gaussian distribution is white noise for sure. Editing it now. Sep 29, 2018 at 14:45
• Yes but I thought that distinction may help clear up your confusion in “not looking the same”... in that even a set with just two elements can be used to generate a white noise sequence. Sep 29, 2018 at 14:47
• (I have never seen the term used but I am guessing in that case it would be "AWBN"!) Sep 29, 2018 at 14:57