Resonant Frequency: Article Archive

This is an old Usenet Newsgroup post that I found on Deja.com. I was familiar with White and Pink noise, but this explains a few other "colors" of noise.
I've had a number of people contact me about making corrections to this list. I've put these changes at the bottom of the page instead of in the middle of the orignal post.

From: Joseph S. Wisniewski
Newsgroups: comp.dsp,comp.sys.ibm.pc.soundcard.tech,comp.speech,alt.sci.physics.acoustics
Subject: The colors of noise 1.3
Date: Mon, 07 Oct 1996 08:22:31 -0400

That email just keeps coming in. So, here's the latest rev. Thanks to the many people who pointed out the flaws in my pink and blue definitions. Thanks Kev fot the pointer to FS-1037C. Due to popular demand, I am reversing my previous stand and adding the definition of orange noise.

The noises are now in spectral order (artistic license has been taken over where white, black, grey, and brown fit into a spectrum). Anyone is welcome to help fill in the gaps. We're up to three defintions of black noise. Keep them coming!

White noise (common definition) power density is constant over a finite frequency range. AKA Johnson noise.

Pink noise (common definition) power density decreases 3dB per octave with increasing frequency (density proportional to 1/f) over a finite frequency range which does not include DC. Each octave contains the same amount of power. Many point out that this is not a trivial filtering problem. (The side effect is flicker noise).

Red noise (common definition within the oceanographic field, contributed by P.J. "Josh" Rovero) (Anyone have the spectrum?) Oceanic ambient noise (ie, noise distant from the sources) is often described as "red" due to the selective absorption of higher frequencies."

Orange noise (anonymous contribution) (Anyone foolish enough to want the spectrum?) Quasi-stationary noise with a finite power spectrum with a finite number of small bands of zero energy dispersed throughout a continuous spectrum. These bands of zero energy are centered about the frequencies of musical notes in whatever system of music is of interest. Since all in-tune musical notes are eliminated, the remaining spectrum could be said to consist of sour, citrus, or "orange" notes. Orange noise is most easily generated by a roomfull of primary school students equipped with plastic soprano recorders.

Green noise (defined by some folks producing relaxation tapes, Mystic Moods, I believe) supposedly the background noise of the world. A really long term power spectrum averaged over several outdoor sites. Rather like pink noise with a hump added around 500Hz. (Anyone have the spectrum?)

Blue noise (FS-1037C) power density increases 3dB per octave with increasing frequency (density proportional to f) over a finite frequency range. This can be good noise for dithering.

Purple noise (origional definition, contributed by Jon Risch) power density increases 6dB per octave with increasing frequency (density proportional to f^2) over a finite frequency range. Differentiated white noise. AKA violet noise.

Grey noise (heard this one a couple of times, but can't put my finger on a source) noise subjected to a psychoacoustic equal loudness curve (such as an inverted a-weight curve) over a given range of frequencies, so that it sounds like it is equally loud at all frequencies. This would be a better definiton of "white noise" than the "equal power at all frequencies" definition, since real "white light" has the power spectrum of a 5400K black body, not an equal power spectrum.

Brown noise (Jon M. Risch, rbmccammon) power density decreases 6dB per octave with increasing frequency (density proportional to 1/f^2) over a frequency range which does not include DC. Is not named for a power spectrum that suggests the color brown, rather, the name is a coruption of Brownian motion. If we were going to pick a color, red might be good since pink noise lies between this noise and white noise. Unfortuantly, red is already taken. AKA "random walk" or "drunkard's walk" noise.

Black noise

There's Three different definitions of black (silent) noise:

contributed by Jeff Mercure, his own definition: whatever comes out of an active noise control system and cancles an existing noise, leaving the world world noise free. (The comic book character "Iron Man" used to have a "black light beam" that could darken a room like this, and popular SCI-FI has an annoying tendancy to portray active noise control in this light.)
Seen in the sales literature for an ultrasonic vermin repeller: power density is constant for a finite frequency range above 20kHz. Ultrasonic white noise. This black noise is like the so-called "black light" with frequencies too high to be preceived as sound, but still capable of affecting you or your surroundings.
Manfred Schroeder, "fractals, chaos, power laws," contributed by Mike Arnao - has an f ^ -beta spectrum, with beta > 2, and is characteristic of "natural and unnatural catastrophes like floods, droughts, bear markets, and various outrageous outages, such as those of electrical power." further, "Because of their black spectra, such disasters often come in clusters."

Changes and Corrections

Below is a list of emails and SDIY newsgroup posts about this article. Each author's reply is seperated by a horizontal bar.

There are inconsistencies throughout the page and I've seen literature describe 1/(f^2) noise as red, not brown. The page says that 'purple noise' is differentiated white noise, but if white noise has a distribution of 1, then differentiating it gives you 0 (silence).

I think it should go something like this:
'infrared noise', 1/(f^3) distribution
'red noise', 1/(f^2) distribution
'pink noise', 1/f distribution
'white noise', unity distribution
'blue noise', f distribution (given on page)
'violet noise', f^2 distribution
'ultraviolet noise', f^3 distribution

The black noise distribution seems consistent in keeping with the light/sound analogy.

Ryan

Well, that it is called "white noise" is just the Brownian noise, which is due to the Brownian motion of particles. This is by its nature also called thermal noise, since the Brownian motion of atoms is due to their temperature (which is a measure on how much Brownian motion they have).

Brown discovered this form of motion when investigating particles in his microscope. The first observation of this noise in electronics components is due to J.B. Johnson of Bell Telephone Laboratories in 1927 and the theoretical analysis was delivered the next year by his colleague H. Nyquist.

This noise has a flat power spectrum in theory. As you know reality deviates only slightly from theory, but we usually ignore the discrepance. ;O)

The so belowed "pink noise" is also known as excess noise, current noise and even flicker noise (due to the flickering effect in tubes).

Then the "red noise" is the 1/f^2 noise.

Also, we have shot-noise, wich has even worse degree (I don't recall now if it was 1/f^3 or 1/f^4). I think "brown noise" sometimes have been used to describe shot-noise.

"blue noise" could possibly be described for a f power-spectrum and "purple noise" would then be f^2 I'd guess. I haven't seen any conclusive definitions on these as I see it.

As for filtering, for a 1/f^2 we have an integrator (with respect to time), f^2 is a diffrentiation (with respect to time). 1/f and f variants are harder. The 1/f is a "half-pole" integrator and the f is a "half-zero" diffrentiator. For those we only make approximations. Cheers,
Magnus