Talk:White noise

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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)
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