Talk:Pink noise

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There is much interest in the source, nature, effect, and suppression of low-frequency noise, however you don't hear much talk about the use of 1/f noise to excite target phenomena.

For example, soothing music is said to contain 1/f noise; what woud be the effect if the level of 1/f in said music was increased by artificial or natural means? more soothing?

Experiments on human subjects have been done for reducing blood pressure simply by staring at a flickering candle flame. Would the candle flame not be a rich source of 1/f "noise". I know that it is soothing to me when my blood pressure drops, so perhaps that is the effect of the candle flame and music.

I think it might also be true that if a person was placed in an environment where there was no 1/f present whatsoever (to any of the five senses), that person might go stark, raving mad?

-Charles Trotter, Consultant (Definition of Consultant: Someone who knows about the same as everyone else but has it organized and gives slide shows.)

1 Reducing ambient noise
2 White vs pink
3 The noise of financial markets?
4 True pink noise
5 References
6 Split
7 1/f noise: some clarifications and a rename/merge proposal
- 7.1 Update & merge proposal
8 Flicker noise merge
9 Natural images, and the number of dimensions
10 Hooge noise

[edit] Reducing ambient noise

i've heard of the use of pink noise in reducing ambient noise, as pink noise would maskerade human voice. Like a silencer. Is it true? If it is it should be pointed in the article.

-alexandre van de sande

alexandre, the use of noise (white, pink, etc.) to mask other sounds is often misunderstood/overrated. trusting a noisemaker for masking can in some cases have the opposite of its intended effect. for example, i recall seeing a film where a psychologist turned on a small nearby noisemaker prior to a session with a client, with the intention of keeping those in nearby rooms from following their conversation.

"small" is important there, because it means the noise probably won't have much low end; therefore, it won't go through walls very well. "nearby" is even worse, because if the noisemaker is close to them, the result will be that they talk louder to hear themselves over the noise. somebody in a room might then hear them better with the noisemaker than without.

almost any noise of moderate bandwidth can mask other sounds near the same frequencies. white and pink noise are often used because they are at constant levels, not having pauses through which the protected sounds may be discerned. an argument can be made that a better masking source would have some irregular nature to it, making it harder for a determined listener to tune out. the level, however, should remain mostly consistent. in any case, the locations of the sound sources and the potential listeners are crucial.

in the above example, the psychologist and his client would be better off moving toward the center of the room (away from walls and vents), and placing low-to-mid frequency noise sources along every wall and vent through which they don't want their conversation heard. that way they will keep their voices low (being further from the noise), and the relative mix downstream will have more noise in it, not only because of the new mix inside the room (more noise than voices), but because the low and mid frequencies will go through the walls better, and because the noise source is now closer (therefore louder) than the voices.

an even better example, though crude, is the behavior of folks using the toilet when a loud fan is overhead. they have the illusion that people outside hear the same mix they do. however, much of the fan's noise (mid-to-high frequency) is masked by the door and walls, whereas the, um, "natural" sounds are quite audible, and sometimes even louder than they would be if the donor didn't have that loud fan in his ears. a similar example is how people try to hold conversations with somebody running water at a kitchen sink; the proximity of the running water makes it hard for the person at the sink to hear, whereas the noise:voice mix for the person across the room is negligible.

re "silencer", the use of that word in this context is misleading. masking can only silence things relatively. the overall level is always increased, unless anti-noise is the masking source. however, though anti-noise works great in headsets and other tightly controlled environments, it's far more position dependent then brute force masking (drowning out), and isn't the panacea it's often portrayed. SaltyPig 06:25, 10 Jan 2005 (UTC)

[edit] White vs pink

SaltyPig, from our edit summaries we both feel we have corrected the article, though our edits appear to be the opposite. Please explain where I am wrong. Hyacinth 18:31, 9 Jan 2005 (UTC)

major correction: The human auditory system...does not perceive equal magnitude at all frequencies, thus whitwhite noise is not perceived as white noise, but pink noise is." -- Hyacinth 15:00, 11 Aug 2004
"The human auditory system...does not perceive equal magnitude at all frequencies..." section. incorrect -- SaltyPig 01:30, 9 Jan 2005

Well, we hear according to the Equal-loudness contours, right? - Omegatron 19:56, Jan 9, 2005 (UTC)

hi, Hyacinth. please excuse if i've stepped across wiki protocol. i don't have much experience with contested edits. glad you brought it up. the logical conclusion from acknowledging the distortion of the human ear is that nothing is heard as it is, rendering moot the pointing out that we don't hear one certain thing as what it is. what's crucial is that we hear white noise as our version of white noise; we recognize it for what it is. we can tell the difference between that and pink noise. should we say that we don't hear a cat's meow as a cat's meow until it's been run through an arbitrary filter to make it closer to what a mic hears?

the previous version asserted that "white noise is not perceived as white noise, while pink noise is." does that mean pink noise is perceived as white noise, or pink noise is perceived as pink noise? either way, it's incorrect. pink noise is not adjusted accurately for the human ear. if there's a color of noise (say for example, "fletcher-munson-bark") which is adjusted for the human ear, it might be worth a mention. however, it would still be misleading to say that "fletcher-munson-bark noise" is perceived as white noise.

let me know what you think of that. and please feel free to revert until we clear this up. my overall feeling is that the paragraph is unnecessary. whether your version or mine, i'd like it removed. pink noise has no direct bearing to bark, fletcher-munson, et al, nor should we forget that all such quantifications of human perception are arbitrary, and hardly suited to equating with such a tightly specified, verifiable thing as pink noise. SaltyPig 22:48, 9 Jan 2005 (UTC)

It's worth noting that '1/f noise' is not limited to sounds like the samples played on the site. Music and speech both have 1/f noise spectra (Voss & Clarke, 1975). —WebDrake 12:09, 20 April 2006 (UTC)

[edit] The noise of financial markets?

1/f noise is found in a wide variety of physical phenomena. Examples include ... financial markets, astronomy, and human coordination.

What exactly does it mean for financial markets, astronomy, and human coordination to produce noise? Obviously this isn't talking about physical sound (stars don't make sound that travels through space), but since the article does appears to be talking about sound, this should be made clear. — Asbestos | Talk 10:03, 14 Apr 2005 (UTC)

'Noise' is a meaningful term with respect to all signals, not just sound. The original discovery of 1/f noise was in current fluctuations in vacuum tubes (Schottky, 1918, 1922; Johnson, 1925). With respect to financial markets you can look at e.g. volatility (fluctuations in the amplitude of price movements): the autocorrelation shows power-law decay. I'll try to add some references here. —WebDrake 11:58, 20 April 2006 (UTC)

[edit] True pink noise

I have some problems with the recent entry. It says:

"Producing true pink noise is notoriously difficult. Most digital and analog "pink noise" generators don't produce mathematically perfect 1/f noise; instead they start with white noise and filter it to remove more and more energy at succesively higher frequencies (about 3 dB per octave). This produces a more or less acceptable approximation to pink noise, depending on how many filters are used, but true pink noise cannot be produced from white noise with a finite set of filters."

Producing "true" pink or white noise is impossible - it would require infinite energy to generate the high frequencies all the way out to infinity. That means that these faulty pink noise generators don't start with true white noise to begin with. When you say that it takes a number of filters, you must be talking about a practical limitation, not a mathematical one. If you had the right kind of filter, and you had noise that was white over the bandwidth of interest, you would only need one filter. So when you talk about a number of filters, you must be talking about a specific kind of filter. Which kind? PAR 05:43, 25 September 2005 (UTC)

Good points. Why don't you be bold and fix the article? —Keenan Pepper 12:54, 26 September 2005 (UTC)

Ok - I did. PAR 02:06, 29 September 2005 (UTC)

[edit] References

I've expanded the reference list. It now includes both of Schottky's early papers in the Annalen der Physik as well as Johnson's 1925 Physical Review paper, which I think is the earliest English-language reference. I've also included the Press (1978) and Dutta and Horn (1981) reviews, and a recent review of scale-free biological phenomena.

With regard to 1/f noise in neural signals, it's probably worth looking at the work of Walter J. Freeman: if anyone can get hold of Mass Action in the Nervous System (Academic Press, New York, 1975), that might contain appropriate data. Another one, which I'll try to get hold of, is in Brain Res. 65, 91–107. (1974). I have some of his more recent papers, but they are simulation papers, not the original data. Funnily enough the Gisiger review does not reference them. I'll look around and see what else I can find.

The William H. Press review covers at least some of the astrophysics and other data. As for financial markets etc., again, I'll see what I can find that feels appropriate. If anyone knows of a more recent, comprehensive review of 1/f noise, that would be very helpful.

One brief note — I've kept the Schottky papers because they were already referenced (and are historically important), but from my understanding they are not actually on 1/f noise. My impression is that Schottky discovered the existence of fluctuations in the current, and theorised that they should be white noise: Johnson (1925) measured the effect more precisely and showed the 1/f phenomenon. This is implicit in Johnson's paper and also the "pedagogical review" by Milotti, but I would like confirmation (I've tried and failed to get the Schottky papers out of Wiley).

Cheers, —WebDrake 13:05, 20 April 2006 (UTC)

[edit] Split

"Pink" is a word to describe the character of noise, and is unrelated to its source or the medium it exists in. It's just a description of the noise's frequency content. For instance, statistics of natural phenomena can be pink without involving electronics at all.

"Flicker" noise is a specific phenomenon found in electronic circuits, which happens to have a pink spectrum. Flicker noise should not redirect here. — Omegatron 14:06, 1 September 2006 (UTC)

If you want to write a detailed article on flicker noise, that's fine with me. —Keenan Pepper 16:15, 1 September 2006 (UTC)

Well, I'll start it, anyway. :-) — Omegatron 17:00, 1 September 2006 (UTC)

Oh good! I was worried it would languish as a stub, but it looks quite decent. —Keenan Pepper 21:45, 1 September 2006 (UTC)

Actually, I would like to propose it come back into the main pink noise article, for reasons discussed on Talk:Flicker noise. Basically I feel that we can do the particular subject justice in the present article, and also that both subjects gain from being included together: flicker noise, from being discussed in the wider context of possible 1/f noises, and pink noise, because flicker noise is one of the most important historical examples. —WebDrake 22:16, 28 December 2006 (UTC)

[edit] 1/f noise: some clarifications and a rename/merge proposal

First of all, a query: can someone who knows about this side of things clarify whether "pink noise" refers generally to noise with a $1 / f α$ spectrum (at least within the range $\alpha \in [1,2)$ or whether it refers to strict 1/f noise ( $α = 1$ only)?

I have the impression that the term "pink noise" is only really used in the context of acoustic noise, can anyone comment on this as well?

More generally, I would propose that this article be renamed 1/f noise, and Brownian noise should be merged into it, with "pink noise" and "brown noise" being subsections of a more general, larger article on all noises with a $1 / f α$ spectrum.

Thoughts? —WebDrake 01:06, 29 December 2006 (UTC)

I've always known pink noise to be strictly 1/f, used in any context; acoustic or otherwise, and definitely distinct from Brownian noise. For an article that summarizes everything with a

1 / f α

spectrum, see Colors of noise. — Omegatron 07:00, 29 December 2006 (UTC)

No, that article is inadequate to what I have in mind.

1 / f α

noise occurs in nature with a variety of

α

values; strict exponents of 1 or 2 are only two possibilities. For example if you look at the flicker noise review by Voss and Clarke (1976) they cite exponents varying between 1.0 and 1.4. What makes

1 / f 2

noise distinct is that it is simply integrated white noise, so not necessarily a reflection of a complex underlying process. If we look at the items cited in the pink noise article not all of them have spectra with exponents precisely 1. It follows that if pink noise has such a strict interpretation this is an inappropriate title for the article. —WebDrake 19:15, 31 December 2006 (UTC)

Then those items don't belong in this article. — Omegatron 19:37, 31 December 2006 (UTC)

The article really discusses 1/f noise (a term which is used in my experience to refer to any noise with a

1 / f α

spectrum) in general, and does so quite well. I propose it should be renamed accordingly and "pink" noise be noted as a special case. —WebDrake 11:43, 1 January 2007 (UTC)

a term which is used in my experience to refer to any noise with a $1 / f α$ spectrum

Aha. You think that "1/f" actually means "1/f^α"? Why do you think that? I'm pretty sure "1/f" just means "1/f". "1/f noise falls off at 3 dB per octave", for instance. — Omegatron 16:25, 1 January 2007 (UTC)

I think that because it is my experience based on reading the scientific literature. For example if you read the review by Dutta and Horn cited in the main article, they use the term "

1 / f

noise" in the title, but as the text of the article makes clear, they actually address noises where the spectrum has a variety of different exponents between 0.9 and 1.4. You might also see Voss and Clarke (1975, 1976), in Nature and Phys. Rev. B. —WebDrake 22:16, 1 January 2007 (UTC)

Further to the above, a quote from Marvin S. Keshner (1982). "

1 / f

noise". Proceedings of the IEEE 70: 212–218.

The $1 / f$ noise is a random process defined in terms of the shape of its power spectral density $S (f)$ . The power or the square of some variable associated with the random process, measured in a narrow bandwidth, is roughly proportional to reciprocal frequency:

$S(f) = \frac{\textrm{constant}}{|f|^{\gamma}}$ where $0 < γ < 2$

and $γ$ is usually close to 1.

I don't think you could have a clearer demonstration of the broadness with which the term is used. Many 1/f noise sources indeed have exponents of 1 or close to 1 but it is not the definition.

Now we need to address the question: is "pink noise" synonymous with 1/f noise in this sense, or does it strictly mean an exponent of 1? I suspect the former, since in colour terms after all, pink may be paler or darker. —WebDrake 15:13, 2 January 2007 (UTC)

So most define pink noise as exactly 1/f, and others loosen the definition to apply to naturally-occuring noise sources that are "roughly proportional" to 1/f. I don't see what the problem is. — Omegatron 18:46, 2 January 2007 (UTC)

There are several issues. One is that I believe the term "1/f noise" to be much more widespread than "pink noise". Second, if pink noise is so strictly defined (which it might be, since most definitions I've read on the web refer to equal energy per octave), most natural 1/f noises do not conform to this definition and we should rewrite appropriately. Third, it would be nice to have the concept of

1 / f α

noises discussed collectively in a manner that goes beyond what Colors of noise does. The "colours" are a rather vague way of discussing the issue. —WebDrake 19:04, 2 January 2007 (UTC)

One is that I believe the term "1/f noise" to be much more widespread than "pink noise".

I'd say it's the opposite. :-) Google test says "pink noise" is 1.3 times as popular, but that's not conclusive.

Second, if pink noise is so strictly defined (which it might be, since most definitions I've read on the web refer to equal energy per octave)

I think it is.

most natural 1/f noises do not conform to this definition and we should rewrite appropriately.

Should probably just be in its own section.

Third, it would be nice to have the concept of $1 / f α$ noises discussed collectively in a manner that goes beyond what Colors of noise does.

That would be better in another article, but what would it contain that's not in the colors of noise article? — Omegatron 19:43, 2 January 2007 (UTC)

Try searching on Google Scholar and "1/f" comes out on top, winning not simply in absolute numbers but by an order of magnitude. 1/f is the scientific term. ;-)

I think the "colors of noise" article gives a simplistic interpretation of a complex phenomenon. Most naturally occurring noises do not have power spectra that follow an integer power of f. Mandelbrot and Van Ness suggested the term "fractional noise", in analogy to fractional Brownian motion, to reflect this (I've since seen "fractal noise" used with similar intent).

I suggest that I take the existing 1/f noise page and replace the redirect with a writeup along the lines of what I want. If it works out we can make appropriate alterations to pink noise, brown noise and colors of noise. I will do my best to make minimum disturbance to the existing structure of the noise pages, for the time being (we may end up making major changes, but I won't force them:-). Sound all right? —WebDrake 20:04, 2 January 2007 (UTC)

Try searching on Google Scholar and "1/f" comes out on top, winning not simply in absolute numbers but by an order of magnitude. 1/f is the scientific term. ;-)

Ok. :-)

I suggest that I take the existing 1/f noise page and replace the redirect with a writeup along the lines of what I want. If it works out we can make appropriate alterations to pink noise

I think 1/f noise and pink noise are closely enough related that they should be the same article. Either move this article to 1/f and rewrite it, or do as you suggested and overwrite this article when you're done. I don't think we should have separate articles for each term.

I think the "colors of noise" article gives a simplistic interpretation of a complex phenomenon. Most naturally occurring noises do not have power spectra that follow an integer power of f.

I'd say the noise colors are simple and well-defined integer powers, while the naturally-occurring noises are grouped into whatever color bin they are closest to. "The noise caused by x is approximately pink", for instance. The colors of noise article is mostly meant to define the various terms and, I hope, will someday explain where they came from as well. It originated from an unsourced newsgroup posting that was passed around for several years, and I think has improved drastically in comparison.

Mandelbrot and Van Ness suggested the term "fractional noise", in analogy to fractional Brownian motion, to reflect this (I've since seen "fractal noise" used with similar intent).

Fractional noise could be a very good place for this, linked to from the second paragraph of Colors of noise. We already have Fractional Brownian motion. — Omegatron 20:30, 2 January 2007 (UTC)

Sadly "fractional noise" would not be a good term, as the name never caught on.

I will use the 1/f noise page for now and, when done, we can decide whether to merge back into pink noise or replace pink noise with a redirect. —WebDrake 20:35, 2 January 2007 (UTC)

I see a lot of references to "fractional noise". It's ok to use a less common term for an article title if it's more accurate than the more common term. I don't think we should have an article called "1/f noise" that's actually about "1/f^β noise". — Omegatron 21:44, 2 January 2007 (UTC)

With what search? Searching Google Scholar for "fractional noise" (including quote marks, so searching for the phrase) gets just 644 pages, compared to around 2700 for "pink noise" and about 17,000 for "1/f noise". It's not a term used in science in my experience. —WebDrake 00:26, 3 January 2007 (UTC)

[edit] Update & merge proposal

I note that someone removed the redirect from 1/f noise, which was unfortunate, because I had not yet brought the proposed article to a high enough standard.

Can I suggest that we do not yet merge anything one way or the other, but take the time to finish the new article, then decide how we want to proceed? In the meantime it might be better to reinstate the redirect while 1/f noise remains incomplete.

Comments on what has been written there so far would be welcome. —WebDrake 23:10, 17 January 2007 (UTC)

All types of noise of the form 1/f^a where a>=0 should be included in one all encompassing article about noise regardless of the source of the noise. Within the main article you can have sections on specific types of noise and their sources. That way if someone is looking for a specific type of noise but doesn't know what it's called they can go to the main article and read it until they find a description that fits their needs. For example I had never heard of flicker noise, although I have heard of electronic pink and white noise, until I went to the article on Pink Noise and saw the merge recommendation box at the top. Dr. Morbius 23:58, 16 February 2007 (UTC)

We have Colors of noise, which already mentions it:

Many of these definitions assume a signal with components at all frequencies, with a spectral density per unit of bandwidth proportional to 1/f^β. For instance, white noise is flat, with β = 0, while brown has β = 2.

I think that would be the most appropriate place for an all-encompassing article. — Omegatron 16:46, 13 March 2007 (UTC)

[edit] Flicker noise merge

Flicker noise was explicitly split from this article because it's a different topic (a type of noise that happens to be pink). I obviously oppose a merge. — Omegatron 01:59, 12 January 2007 (UTC)

I oppose as well. Flicker noise is a particular (distinct) type of pink noise.--Srleffler 03:14, 13 January 2007 (UTC)

[edit] Natural images, and the number of dimensions

Is it a big bug? I think the article is in error concerning the statistics of natural images. It states that natural images should have a 1/f spectrum (and from the text at the beginning it should be clear that this would apply to the power spectrum). But when reading the cited literature (and it is easy, just click the link) I find on page 2385, just below Fig. 7: "The amplitude falls off quickly by a factor of roughly 1/f (i.e., the power falls at 1/f²)." So either the definition of pink and Brownian (red) noise is incorrect, or natural images have a Brownian (red) noise power spectrum. Kaernbach 21:36, 10 July 2007 (UTC)

I just verified with David Fields himself. And I got a very interesting answer. It is a question of the number of dimensions. Pink noise (which is self-similar on scaling) is 1/f in one dimension (acoustics), and 1/f^2 in two dimensions. The same is true for Brownian noise: 6 dB/octave in 1 dim, 12 db/octave in 2 dim (always referring to the power spectrum). So the reference to Fields (1987) is correct in the pink noise article, but the definition of pink noise should include the number of dimensions. Is there anybody volunteering for this change? Or should I? Kaernbach 17:53, 30 July 2007 (UTC)

[edit] Hooge noise

I found another name for this noise to be "Hooge noise", so I redirected it to this artcle. If that is something different, just let me know,--Rayc 18:10, 3 October 2007 (UTC)