[sdiy] Various colors of noise.

[brianw]

The probability distribution of the values in a random sequence are completely independent of the frequency spectrum of those values as a signal.

First order probability distribution is uniform, and this is what the simplest mathematical computer noise sources produce. Second order is Triangular Probability Distribution Function (TPDF), or the sum or average of two uniform sources. Increasing the order to infinity yields Gaussian distribution, which is how nature presents values for most things, like Brownian motion, i.e., resistor noise, and that's probably why it's called "normal distribution." Chapter 2 of The Scientist and Engineer's Guide to Digital Signal Processing gives a shortened formula for creating a Gaussian distribution from two uniformly distributed values (rather than an infinite series).

These distributions of noise all seem to sound the same when implemented, but if used in a process as a modulator, then the derivative of the probability distribution may affect the sound, making higher order distribution "curves" less objectionable.

I assume that most nature sounds are attenuated according to distance, with high frequencies falling off faster than lower frequencies. I recommend investigating Stokes law of sound attenuation.

Anyway, I suspect that all nature sounds start with normal distribution and are simply filtered by the air. I would not bother with too complicated a filter if you only want ambient sounds.

Brian


On Mar 2, 2026, at 6:15 PM, Thomas Hudson wrote:
> Yes very much different. There’s an old article in Scientific American by Marvin Gardner, that shows that music statically follows 1/f  or pink noise.
> 
> Note selection by red or brown noise is very boring. Imagine you have a random set of five dice to select the next note. Red / brown is only rolling  one of the dice for every selection.
> 
> Random sampled noise at any specific color frequency still follows the statistical likelihood of the next sample for that color..
> 
> There’s great way to hear the difference:
> 
> -  Colored noise, clocked sample / hold, quantizer, note selection.
> 
> The note selection differences are very apparent.
> 
> Though it would be interesting to plot the curves at various sample rates.
> 
> On Mar 2, 2026, at 8:31 PM, Emily Straight <emily.tw.straight at gmail.com> wrote:
>> is there any statistical difference between different colors of noise after going through a sample-and-hold? i'd figured on longer timescales every possible voltage is equally likely anyway, so you wouldn't be able to tell the difference.
>> 
>> On Mon, Mar 2, 2026, 3:26 PM Thomas Hudson wrote:
>>> I have an analog module that can generate blue, white, pink, and red (brownian) noise. I’m interested in how I might create a random walk using perhaps a sample/hold and smoothing function to produce a sort of wandering control voltage from each of these noise sources.
>>> 
>>> I also was recently introduced to green noise. From Wikipedia:
>>> 
>>> 	• The mid-frequency component of white noise, used in halftonedithering[19]
>>> 	• Bounded Brownian noise
>>> 	• Vocal spectrum noise used for testing audio circuits[20]
>>> 	• Joseph S. Wisniewski writes that "green noise" is marketed by producers of ambient sound effects recordings as "the background noise of the world". It simulates the spectra of natural settings, without human-made noise. It is similar to pink noise, but has more energy in the area of 500 Hz.
>>> 
>>> Wondering how I might generate this other than using something like a bandpass filter tuned to 500 Hz using pink noise. I want to generate it in the analog realm.
>>> 
>>> TIA,
>>> Thomas
>