Talk:White noise

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HOLY FUCK SOMEONE GIVE A FUCKING WARNING ABOUT HOW LOUD THAT WHITE NOISE SAMPLE IS YOU PIECES OF SHIT I ALMOST HAD A HEART ATTACK AND I CANT HEAR 76.101.72.59 16:00, 3 December 2007 (UTC) Need some clarification on this statement:

"I.e., it is a zero mean process for all time and has infinite power at zero time shift since its autocorrelation function is the Dirac delta function."

Shouldn't it be as follows:

"I.e., it is a zero-mean process for all time and has infinite average noise power since its autocorrelation function is the Dirac delta function at zero time shift"?

R_{xx}(0)=E[X^2(t)]=\infty -User:Daniel.Kho

Agree. White noise is not necessarily gaussian, and gaussian noise is not necessarily white. I found this article and discussion extremely useful. However, I would like to suggest that some of the experts around here edit the article on Additive White Gaussian Noise since it is noise that is both white AND gaussian. I feel the AWGN article is very much lacking on a lot of things. User:Daniel.kho

White noise does not necessarily have a normal distribution (if generated by a random number generator, it's uniform or has two equal spikes), nor is noise with a normal distribution necessarily white (normal white noise passed through a pink filter becomes normal pink noise). -phma

I find the following paragraph from the original article a little unclear:

"It is often incorrectly assumed that Gaussian noise (see normal distribution) is White Noise. The two properties are not related. However, Gaussian White Noise is often specified; such a signal has the useful statistical property that it's values are independent in time."

Does the "Gaussian noise" referred to mean Gaussian in the frequency spectrum, thus not white because by definition white noise has flat frequency spectrum?

Is not "Gaussian white noise" a random signal which (a) has a Gaussian probability density function (in time), and (b) is uncorrelated in time (thus white because it has a flat frequency spectrum)?

What is meant by "independent in time"? Is this the same as uncorrelated in time? Uncorrelated in time -> random, but does NOT mean/imply Gaussian. -drd

Fixed up the math a bit, does this still need to remain flagged for peer review to address the rest of these questions? --carlb 14:04, 13 Oct 2004 (UTC)

It would be nice if someone who is familiar with the concept answers the questions above. They are not covered explicitly in textbooks. The article alludes to whether the Gaussian distribution is in the time-domain, but is not explicit. --vlado4 21:51, 12 November 2005 (UTC)

Can someone please discuss what "colored noise" is! I googled the term and it provided only vague results... Please, Please, Please,Please, Please, Please, Please! Ved 01:33, 23 January 2006 (UTC)TRUPET

Are you after Colors of noise? -Splashtalk 01:43, 23 January 2006 (UTC)

Contents

[edit] Gaussian noise

Indeed, for Gaussian noise a value at any one time-point will come from a Gaussian distribution. This does not say anything about what happens if you pick two values from adjacent time-points -- if the two values from adjacent time-points are always similar then you have pink noise, and if they are uncorrelated you have white noise. Both can be Gaussian noise, however. Rnt20 08:47, 10 Mar 2005 (UTC)

[edit] Simulating a random vector

Suppose that a random vector \mathbf{x} has covariance matrix Kxx. Since this matrix is Hermitian symmetric and positive semidefinite, by the spectral theorem from linear algebra, we can diagonalize or factor the matrix in the following way.

\,\! K_{xx} = E \Lambda E^T

What is the Lambda? A Definition of the Lambda is missing!

It's defined in the next sentence. PAR 14:59, 18 October 2005 (UTC)

[edit] Sleep Aid or Sleep Deprivation?

The article states that it's used in torture, and the torture article backs it up, but isn't it quite well-known that a lot of people need white noise to sleep, as it blocks out other noises and is very easy to block out?

It is unikely that anyone uses white noise to sleep, while it is in a mathematical sense "natural", it is definitely not something humans have evolved to find pleasant or easyto block out because it has all those frequencies which aggitate us to alertness (as well as all other frequencies of course) and frankly hurt our ears. This makes sense when you think about the fact that such a purely stochastic process which would generate white noise would be rare in nature and therefore we wouldn't have evolved in a way that would make us tolerant of it--but have evolved to be agitated by several of the frequencies which it contains. Brown noise would be a much more likely canidate for that, as it contains the frequencies which we are most used to hearing (because its the frequencies that wind, water, and rustling vegetation tend to generate). If you listen to white noise you'll see what I mean,it is very grating, whereas brown noise can be soothing. --Brentt 04:38, 13 January 2006 (UTC)

[edit] Applications

The article says that white noise is used because: it cuts through traffic noise and doesn't echo. All sound echos, its just that the echo mixes in so you can't distinguish it.

And white noise is used in sirens because of the range of frequencies. The human mind is better able to distinguish the direction of multi-frequency sound over the standard mono tone sirens.

It is the simple volume and uniqueness of a siren that makes it cut through traffic noise. When white noise is used in a siren it is usually a part of or underlying the sound of the usual mono-tone as it is actualy harder to distinguish from traffic noise. --Stripy42 19:17, 8 May 2006 (UTC)

[edit] Figures

I feel it might make sense for plots which show white noise 'zoomed in' on to use a 'staircase' view or be generated using the stem() plot function in matlab/octave. As it is, we see linear interpolation between samples; in fact the data shown is no longer white noise, at least not at the sampling frequency implied by the interpolated values. -- Oarih 03:55, 25 September 2006 (UTC)

Agreed. — Omegatron 06:05, 25 September 2006 (UTC)

[edit] Confusing graphic?

I find this graphic a little confusing:

As far as I understand it the graph should be flat, and yet it clearly increases slightly with frequency. I think this needs explaining, or the graphic needs fixing.

[edit] removing image

I am removing the image shown here.

Four thousandths of a second of white noise
Four thousandths of a second of white noise

It adds nothing to the other image. The main problem with it is that because the data points are quite spaced but the image does not explictly indicate the data points, the lines joining the points appear like correlated data, making the noise appear red rather than white. — Alan✉ 05:33, 1 August 2007 (UTC)


[edit] White Noise Not Analogous to White Light

I recommend deleting "White noise is considered analogous to white light which contains all frequencies." White light contains all visible frequencies - a band-limited response of the human eye - whereas white noise contains all frequencies from minus infinity to plus infinity on the frequency scale (i.e., the Fourier transform of a Dirac delta function).
--FP Eblen 17:39, 3 August 2007 (UTC)

It's an analogy, not an identity. Were it to identify a theoretical construct with a physical phenomenon, it would be false, but it merely analogies, and usefully, seems to me. Nobody's got infinite bandwidth. Not EM or sound or noise. It follows that nobody's completely white, just as no real curve is a circle and no real coin has a 0.5 probability of coming up heads, but these theoretical constructs are as useful as the present analogy. Jim.henderson 17:55, 3 August 2007 (UTC)
White noise is distinctly an abstraction, not a real physical entity. It, by definition, has infinite bandwidth. White light is a real physical entity strictly band-limited to the visible spectrum. It is misleading and inappropriate to consider them (even) analogous. If one were describing the concept of a point, it would not be appropriate to say it is analogous to a very small circle, since a point has exactly zero width and a very small circle does not. Same with white noise – its most distinguishing trait is its infinite bandwidth.
This concept is useful and important when considering theoretical systems with widely varying input bandwidths, for example. If white noise is (theoretically) present at the input to the system, one can claim that no matter how wide the input bandwidth gets, the white noise will always fill it. This would not be true if the input was white light.
What makes white noise white and the bandwidth infinite is the fact that its autocorrelation function has non-zero value only for exactly zero shift. For any other value of shift, the autocorrelation function is exactly zero, i.e., it is an impulse function (which, by definition, has exactly zero width). The spectrum of white noise is the Fourier transform of the autocorrelation function, which, being an impulse, makes the spectrum infinite.
Please realize that these are facts which can be corroborated by any textbook describing white noise.
--FP Eblen 22:05, 3 August 2007 (UTC)
Umm, infinite bandwidth is hardly a unique feature of white noise or vice versa. See square and triangular waves, for two examples of the former. Yes, you're right to point out that the relationship between white noise and white light is not an identity. Analogy is not identity, and the current text correctly offers analogy and not identity. Anyway, what alternative text do you offer, in not too many additional words, to make the point (and the meaning of "white" in the context) clearer to readers who do not already understand Fourier transforms, autocorrelations, etc? Jim.henderson 01:48, 4 August 2007 (UTC)
Worse, what we think of as "white" light (e.g., sunlight) is really blackbody radiation, which has a distinct intensity peak in the spectrum according to Planck's law. 155.212.242.34 (talk) 14:16, 7 December 2007 (UTC)
That just means sunlight isn't truly white in the strictest sense. Like many technical terms, "white" has multiple, related meanings. It's ordinary meaning refers to an appearance as perceived by the human eye. This is abstracted to a theoretical source whose power distribution is uniform over all frequencies. Such a source is, of course, a physical impossibility since it would have infinite total power. Practical white noise sources can only approximate whiteness (i.e. uniformity) over some frequency range. In that sense a white noise source and white light are exactly analogous.--agr (talk) 14:46, 7 December 2007 (UTC)
Saying they are roughly analogous maybe okay but not "exactly analogous." The important distinction being that the term "white light" has no implications of randomness whereas "white noise" is white because of its qualities of randomness. Remember the key is that a white noise signal is 100% uncorrelated to itself for any degree of time shift greater than zero, i.e., if one compares a white noise signal to a copy of itself, the correlation is 100% when they exactly overlap in time, but if the copy is shifted an infinitesimal amount (anything greater than zero), the correlation is exactly zero. It is this fact that makes it white since this is what makes the signal spectrum flat and infinite. If the correlation were non-zero for any value of shift greater than zero, the spectrum would not be flat or infinite.FP Eblen (talk) 07:27, 12 May 2008 (UTC)

[edit] removing 'Feral' white noise link

Image:Feral-vs-DigitalWhiteNoise.png

I'm removing the link to www.luketan.com simply because the so-called 'feral' white noise file is not true white noise. You can see the difference between the two here on this image I created. Binksternet 01:15, 25 September 2007 (UTC)

I don't have any invested interest in this particular link, but "white noise" is a colloquial as well as scientific term, meaning noise with a very wide bandwidth that is useful in masking other noise, so I would think this page could accommodate the scientific as well as nonscientific content. I put a link in today for those looking for a source of white noise for masking office noise (my need today). In fact this page is part of sound production technology, and in that context, I would guess the feral stream would be labeled as a "white noise" by most people. If you object, since it's missing mostly high frequencies, maybe just call it pink or nearly white noise. Hess8 16:54, 1 October 2007 (UTC)
I feel the "feral white noise" link would be appropriate at White noise machine and Sound masking but that this page should focus on purely random white noise that has equal power at each frequency. It's enough that White noise machine and Sound masking are mentioned as External links. Binksternet (talk) 17:19, 7 December 2007 (UTC)

[edit] WikiProject class rating

This article was automatically assessed because at least one WikiProject had rated the article as start, and the rating on other projects was brought up to start class. BetacommandBot 10:05, 10 November 2007 (UTC)

[edit] what is N0?!!!

In "White random process (white noise)", the formula references "N0", but gives no definition whatsoever as to what this quantity is supposed to be...65.183.135.231 (talk) 21:24, 4 May 2008 (UTC)