Talk:White noise

message: I've seen many assertions essentially stating that the Fourier transform of Gaussian white noise is also Gaussian white noise, but no proofs, and no specific definition of what that would mean in the complex case.  I understand the explanation given for Gaussian white noise vectors x: 1) the probability density function of x is radially symmetric; 2) the Discrete Fourier Transform is an orthogonal transformation (actually unitary, and it has to be normalized) W so the density function of X=WHx is also radially symmetric.
However, X is now a complex random vector. What is the appropriate translation of a density function in this case?  Do we expect the real and imaginary parts to be Gaussian, or the norm of the components of X?  This gets even harder to decipher when looking at a continuous Gaussian white noise process X_t.
Justin Mauger (talk) 04:22, 25 May 2019 (UTC)
thread_title:  Fourier Transform of Gaussian white noise. 

message: 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
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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
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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
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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)
replies: text: Are you after Colors of noise? -Splashtalk 01:43, 23 January 2006 (UTC)
thread_title:  Untitled comments 

message: Suppose that a random vector \mathbf{x} has covariance matrix K_{xx}. 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)
thread_title:  Simulating a random vector 

message: 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)
thread_title:  Sleep Aid or Sleep Deprivation? 

message: 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)
thread_title:  Applications 

message: 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)
replies: text: Agreed. — Omegatron 06:05, 25 September 2006 (UTC)
thread_title:  Figures 

message: I am removing the image shown here.
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)
thread_title:  removing image 

message: 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)
replies: text: 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)
replies: text: 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)
thread_title: removing 'Feral' white noise link

message: 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)
thread_title:  WikiProject class rating

message: 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)
thread_title:  what is N0?!!! 

message: I took out an external link from a commercial concern which proposes to replace mid-frequency beeping warning tones with white noise. I don't think this external link is useful by itself, though if the concept were developed further as article text it could serve as a reference. Binksternet (talk) 03:10, 18 December 2008 (UTC)
replies: text: Good job. Daniel Christensen (talk) 19:35, 2 November 2009 (UTC)
thread_title:  White noise as vehicle back-up alarm 

message: Despite the name of that image, a flat power spectrum on a logarithmic scale is pink noise, not white.  I have used that image in a couple articles (colors of noise, pink noise) to illustrate pink noise, but it cannot be used for white noise.  If anyone has a correct spectrum, that would be appreciated.  Baccyak4H (Yak!) 18:35, 25 February 2009 (UTC)
replies: text: Update User:Heron fixed this image.  Thanks.  Baccyak4H (Yak!) 19:31, 25 February 2009 (UTC)
replies: text: It's not the scaling of the x axis that makes the difference, it is the method by which the energy is binned. Pink noise in an fft will still fall with freq however the x axis is scaled. I think I got it wrong again in the article. Either way you are confusing things, please stopGreglocock (talk) 01:24, 26 February 2009 (UTC)
replies: text: When pink noise makes for a flat graphic image, such in the live sound application called Smaart or SmaartLive, it is because the data are collected in such a way so as to make that be true. A white noise graph is naturally flat. Binksternet (talk) 03:07, 26 February 2009 (UTC)

text: It is not a matter of wiki-convention, it is a matter of definition. Stretching or compressing the x axis by taking its log does NOT change the vertical scale. If you analyse white noise with a  thrid octave filter (for example) you will get a spectrum that rises at +3dB per octave. If you analyse it with FFT then it will be pretty flat. If you analyse pink noise  with 1/3 octaves you'll get a flat spectrum, whereas the fft spectrum will fall at higher frequencies. Greglocock (talk) 04:34, 26 February 2009 (UTC)
replies: text: It seems we're talking past each other.  We can pick either definition you state, or perhaps even others (if they exist), but in so choosing have now implicitly decided on a convention to use that one.  Hair-splitting aside, the important thing as I see it is to be consistent.  As of now, it appears we have been.  Baccyak4H (Yak!) 16:22, 26 February 2009 (UTC)
replies: text: No, it is not a convention. It is a mathematical definition, there is only one right answer. Greglocock (talk) 02:00, 27 February 2009 (UTC)
thread_title:  power spectrum image flat on log scale == Pink ? 

message: Is this the same as the loud sound of a television channel when there is no signal? Daniel Christensen (talk) 19:34, 2 November 2009 (UTC)
thread_title: TV snow

message: After seeing the extras on dvd, became involved with my studio, as I am also an artist, and images showed up on my computer that are interpretable. Someone might have broken into my data base, and took images, and used them for entertainment, and there were lots of "accidents" and persons won't come forward and say anything. I know how to use images in interpreting modern media, and also use Native American tracing and tracking. Powder *)75.201.143.93 (talk) 22:20, 22 November 2009 (UTC)
thread_title:  White Noise (film) 

message: Right now the article states that "By having power at all frequencies, the total power of such a signal is infinite and therefore impossible to generate.". While white noise does have infinite power, not all signals that have non-zero power at all frequencies have infinite power.130.234.5.136 (talk) 20:35, 23 October 2010 (UTC)
replies: text: I agree with you that there is a problem here. I have taken a stab at improving the paragraph. See if you like it. Binksternet (talk) 20:50, 23 October 2010 (UTC)
thread_title:  Possible inaccuracy 

message: the N_0 is undefined. so I don't understand the formula. Jackzhp (talk) 14:26, 18 January 2011 (UTC)
thread_title: Section 4.2

message: Statistical white noise does NOT need to be iid.  "Weak white noise" is just yt ~ WN(0, sigma^2)"   Strong white noise is yt ~iid (0,sigma^2).  And, as correctly mentioned, Gaussian white noise is yt ~iid N(0, sigma^2)  ("Elements of Forecasting," Francis X. Diebold 4th edition 2007)
:Looking at a couple of books on the net, it seems that the definition and nomenclature varies depending on the author, or perhaps application.  This, by the way, is the rule even in the most abstract mathematical fields.  Do not take any book, no matter how popular, as being the truth in nomenclature and notation.  Wikipedia should try to record all common conventions, without implying that one of them is more "correct" or "official" and any other. Please check the White noise#White noise vector section, it now tries to do that. All the best, --Jorge Stolfi (talk) 21:44, 12 February 2013 (UTC)
thread_title:   statistical white noise  

message: Under Statistical properties is written, "We can therefore find Gaussian white noise, but also Poisson, Cauchy, etc. white noises." I suggest this be changed to, "A Gaussian amplitude distribution could give a white frequency distribution, but so could amplitude distributions that are Poisson, Cauchy, etc.," but am not sure if that covers the meaning of the original sentence. ᛭ LokiClock (talk) 05:47, 23 August 2011 (UTC)
thread_title:  Clarification: Other white distributions 

message: How is the white noise generalized to multiple dimensions?  — Preceding unsigned comment added by 93.173.152.222 (talk) 10:39, 20 February 2012 (UTC)
thread_title:  Generalization to two/n dimensions? 

message: Who is the genius that compressed the white noise image using a lossy algorithm (JPEG)? (hint: it's not real white noise after the compression).
And the genius who put said image in the article?  — Preceding unsigned comment added by 85.74.53.83 (talk) 17:45, 23 August 2012 (UTC)
replies: text: was contributed by . --Kvng (talk) 14:59, 26 August 2012 (UTC)
replies: text: ...And since you can't reproduce the original signal from a spectogram since it is missing the phase information, it makes little odds whether the image is lossless or not. The original complaint was absurd. Greglocock (talk) 22:24, 26 August 2012 (UTC)
replies: text: I'm not endorsing the IP's snark or reasoning but a PNG is generally preferred for screenshots like this. If nothing else, it makes text more readable (though there doesn't seem to be a problem with that here). --Kvng (talk) 13:43, 27 August 2012 (UTC)
thread_title:  Ahem... 

message: " Generating White noise requires outputting a random number through a Digital-to-analog converter. The quality of the white noise will depend on the quality of the Random number generator. There must be a sufficient number of non repeating samples output or else the result will be an audible "
That is a lousy way of generating useful white noise as it will have a uniform amplitude distribution. If the reference in question seriously proposes this method then it is a damn fool reference and should not be trusted. Greglocock (talk) 06:28, 15 September 2012 (UTC)
replies: text: I added a ref which contains details about adjusting amplitude distribution. -—Kvng 13:28, 19 September 2012 (UTC)
thread_title:  Problem with new "Generation" section 

message: Hi, the section White noise#White random process (white noise), like many articles in Wikipedia, seems to be meant for experts who know the notation (a certain notation?) and the jargon used in the field (a certain field?).Each wikipedia article and section should be written in such a way to satisfy all "needy customers" -- readers that come to it because they need the information it contains. In this case, I would think that they would be mostly people (like me) with technical background, who know basic calculus, probability, and statistics, and need to know the basics of "white noise" signals; but are not necessarily familiar with the theory and jargon of stochastic processes.  Those people also would need a bit of justification ("why is the concept defined that way?")Please have a look at this draft proposal for that section. Would it be an improvement? (I am not familiar with the field; I hope it is not complete nonsense.)All the best, --Jorge Stolfi (talk) 03:08, 13 February 2013 (UTC)
replies: text: I took the liberty of correcting a parsing error in your draft (the LaTeX didn't like the minus sign that you used). Sorry I don't know anything about that topic so I can't comment on your draft.  Duoduoduo (talk) 14:47, 13 February 2013 (UTC)

text: Your's is clearly an improvement. It is more accessible and you have included a reference. -—Kvng 16:19, 16 February 2013 (UTC)
replies: text: The definition of continuous-time white noise has been replaced by the draft previously posted.  Please check it.  Is it correct? Is it compatible with commonly accepted definitions? --Jorge Stolfi (talk) 16:45, 27 February 2013 (UTC)
thread_title:  Proposed rewrite of continuous-time white noise section 

message: The section "Random signal transformations" was removed because (a) it seems to be original research and (b) it seems to be incorrect and/or useless.  It is temporarily in :User:Jorge Stolfi/Temp/White noise simulation and whitening until these issues can be resolved.The "whitening" is not possible, even in theory, if the input signal has zero power density at some frequency (or frequency band).  Even if that is not the case, the whitening filter may not be realizable because it may demand unbounded amplification (consider an input signal with Gaussian-shaped power spectrum) or infinite complexity (since the input spectrum may be infinitely complicated).As for the "simulation" part, the name is unwarranted since the 1st and 2nd moments do not constrain the signal very much; hence the shape of the synthetic signal may be totally different from the model signal.  The questions about physical realizability also remain.--Jorge Stolfi (talk) 14:57, 27 February 2013 (UTC)
replies: text: I think you are safe to assign that lot to the bit bucket. It is not appropriate for wiki, even if it is true. Greglocock (talk) 22:47, 27 February 2013 (UTC)
thread_title:  Continuous-time white noise simulation and whitening 

message: Why is white noise also called "static"? Is that derived from "static electricity", and if so, where's the connection? I couldn't find an answer on this in Wikipedia. -- 89.182.88.149 (talk) 08:34, 2 June 2015 (UTC)
thread_title:  "Static"? 

message: It would be good to show the noise pattern both as time and frequency domain. Quaderratistteuer (talk) 19:16, 22 September 2020 (UTC)
thread_title:  Both graphs in time and frequency domain. 

message: Mlm 185.63.219.230 (talk) 22:15, 19 November 2021 (UTC)
thread_title:  Ujn 

message: An editor has identified a potential problem with the redirect :White noise (slang) and has thus listed it for discussion. This discussion will occur at Wikipedia:Redirects for discussion/Log/2022 August 30#White noise (slang) until a consensus is reached, and readers of this page are welcome to contribute to the discussion.  Dronebogus (talk) 11:54, 30 August 2022 (UTC)
thread_title:  "White noise (slang)" listed at [[Wikipedia:Redirects for discussion|Redirects for discussion]] 

message: The redirect Gaussian white noise has been listed at redirects for discussion to determine whether its use and function meets the redirect guidelines. Readers of this page are welcome to comment on this redirect at  until a consensus is reached.  1234qwer1234qwer4 20:51, 5 July 2023 (UTC)
thread_title:  "[[:Gaussian white noise]]" listed at [[Wikipedia:Redirects for discussion|Redirects for discussion]]