Dan Ellis :

About Colored Noise

Following the release of the movie "White Noise", I was contacted by Andy Rathbun, a journalist writing for New York Newsday, who had some questions about the use of colors to describe different kinds of noise. Here are the answers I wrote to his questions, along with links to some sound (and one image) examples - look for the links in the text.

Why are types of noise given color distinctions?

Noise is used to mean a lot of things in engineering, and is an extremely important concept, since a lot of the technical challenges in, say, building a cell phone system, or an ultrasound machine, come from trying to extract a desired information 'signal' from a background of unwanted 'noise'. In general, 'noise' can refer to anything that interferes with what we want: it might be a single voice of someone sitting next to us in a movie, but the 'purest' form of noise comes from a totally random source. In engineering terms, this randomness corresponds to unpredictability: knowing one part of a signal tells you almost nothing about the future of the signal.

This kind of minimum-information noise is called white noise, by analogy with white light which is a uniform mixture of all the different possible colors. In the frequency (Fourier) analysis often used in signal processing, white noise is a uniform mixture of random energy at every frequency.

What is the origin of using colors to distinguish noise?

This analogy then naturally extends to other 'colors'. Just as you can use a piece of colored glass to transform white light into, say, a deep red hue, you can use filters on other kinds of signals to alter the balance of frequency components so that the noise is no longer 'white' but has some other quality. In this case, the signal is still noise, and has very predictability, but it is a little more predictable than white noise, because we know that certain frequencies will be more prominent.

What colorations, outside of white, are used to designate noise?

Any kind of filtered noise signal can be called 'colored noise', which is just to say that it is not a pure white noise. In audio, the most common color encountered is 'pink noise': Realized as sound, white noise sounds like the hiss of an untuned FM radio, or the background noise on a cassette tape player. Because of the particular characteristics of the human ear, the sound of white noise is dominated by the very highest frequencies. To make an audible noise that sounds more as if it is balanced across the full range of audible frequencies, we have to boost the low range (the 'bass' of a conventional stereo) and cut the high frequency; there is still energy at every frequency, but now the balance is shifted. If we were to do the same thing with visible light - which is an electromagnetic wave varying through the colors of the rainbow from red at the lowest frequencies through to blue at the highest frequencies - we would get a pinkish color. Hence this kind of noise is called pink noise. Pink noise sounds more like a hiss mixed with a rumble, like the noise inside a flying passenger jet.

(Red light has a frequency of about 5x10^14 Hz, or about 10^12 times -- a million million, a/k/a a trillion -- higher than the frequencies we can hear. The other big difference between sound waves and light waves is that sound is carried as variations in air pressure, so there is no sound in a vacuum, whereas light, like radio waves, exists as variations in electric field, which exists everywhere - so we can still see distant stars across the vacuum of outer space.)

In audio, you also see references to brown noise, which has an even stronger shift in energy towards the lower spectrum. In fact, the analogy with light would suggest we should call this deep red light, but by a neat coincidence, this kind of noise corresponds to a random-walk process in physics called Brownian motion (after the physicist who described it in 1828), and the color isn't far off. Brown noise sounds like rumbling.

The converse of pink noise, where energy increases for higher frequencies, is called blue noise, again by analogy with light. Blue noise isn't very interesting as a sound (it also sounds like a hiss) but has some important applications in image and video signals.

In general, all noise signals have parallels in the image domain. White noise looks pretty much like the static of an untuned TV set. Some of the more interesting colored noise sequences in images have energy in a limited range of frequencies (analogous to, say, green light) which can look like disordered patterns of ripples in sand or water.

Are the colors used always solid shades or are there gradations of these noise -- say cream, or eggshell?

For pink noise, it doesn't much matter exactly how you map sound frequencies to light frequencies, since the rule is just that the energy decreases steadily with higher frequencies. For more specific colors, we would have to exactly specify the mapping between the two, and in fact there's no good mapping, since the range of visible light frequencies represents less than one factor-of-two or octave (430 trillion Hz to 750 trillion Hz), whereas the range of audible frequencies covers almost ten octaves (about 20 Hz to 20 thousand Hz; one Hz (Hertz) is one cycle per second). So there is no existing convention for mapping more specific colors to particular sounds. In general, the distinctions would not be as interesting acoustically as they are visually - or, at least, a lot of different colors might sound pretty similar, and a lot of sounds which are distinct acoustically might look like pretty similar colors.

Often, CDs offer `white noise' as background sound to relax, like waves lapping on a beach or wind sounds. Is this actually white noise, or is it something else? Is white noise e ven a relaxing sound?

Wind, waves, or similar natural sounds are not exactly white noise - often they are closer to pink noise, but they also have additional modulation. Pure white noise is not particularly soothing, perhaps because it is not something we encounter in nature, and our perceptual systems are acutely matched to the natural world. The advantage of a noise signal is that it can mask out more specific sounds - like the neighbors talking, or cars going by - and submerge them in a steady, continuous sound with no abrupt changes to distract or disturb us. Thus, it makes sense that the closest natural matches to white noise, like the slow undulation of waves at the seaside, can form soothing and effective background noise maskers - a natural sound, but containing no suprises or structure to pull our minds away.

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Dan Ellis <dpwe@ee.columbia.edu>