# What is White noise: Definition + 28 Threads

In signal processing, white noise is a random signal having equal intensity at different frequencies, giving it a constant power spectral density. The term is used, with this or similar meanings, in many scientific and technical disciplines, including physics, acoustical engineering, telecommunications, and statistical forecasting. White noise refers to a statistical model for signals and signal sources, rather than to any specific signal. White noise draws its name from white light, although light that appears white generally does not have a flat power spectral density over the visible band.

In discrete time, white noise is a discrete signal whose samples are regarded as a sequence of serially uncorrelated random variables with zero mean and finite variance; a single realization of white noise is a random shock. Depending on the context, one may also require that the samples be independent and have identical probability distribution (in other words independent and identically distributed random variables are the simplest representation of white noise). In particular, if each sample has a normal distribution with zero mean, the signal is said to be additive white Gaussian noise.The samples of a white noise signal may be sequential in time, or arranged along one or more spatial dimensions. In digital image processing, the pixels of a white noise image are typically arranged in a rectangular grid, and are assumed to be independent random variables with uniform probability distribution over some interval. The concept can be defined also for signals spread over more complicated domains, such as a sphere or a torus.

An infinite-bandwidth white noise signal is a purely theoretical construction. The bandwidth of white noise is limited in practice by the mechanism of noise generation, by the transmission medium and by finite observation capabilities. Thus, random signals are considered "white noise" if they are observed to have a flat spectrum over the range of frequencies that are relevant to the context. For an audio signal, the relevant range is the band of audible sound frequencies (between 20 and 20,000 Hz). Such a signal is heard by the human ear as a hissing sound, resembling the /h/ sound in a sustained aspiration. On the other hand, the "sh" sound /ʃ/ in "ash" is a colored noise because it has a formant structure. In music and acoustics, the term "white noise" may be used for any signal that has a similar hissing sound.
The term white noise is sometimes used in the context of phylogenetically based statistical methods to refer to a lack of phylogenetic pattern in comparative data. It is sometimes used analogously in nontechnical contexts to mean "random talk without meaningful contents".

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1. ### I Noise Whiteness hypothesis in Kalman filtering

In Kalman filter mathematical treatment I have always read that a foundamental hypothesis is represented by the whiteness of the process noise. I have tried to do again the mathematical steps in the Kalman filter derivation but I can't see where such hypothesis is crucial. Could you help me...
2. ### B White noise frequencies and Audio Speakers

Hi everyone . unfortunately for health reasons I have to give it a try and put a pair of audio speakers in my bedroom to reproduce white noise during sleep. I need to know if the audio speakers I already own are able to reproduce the range of frequencies I need, namely that of rain and sea waves...
3. ### Block diagram showing how to turn white noise into rain

So I have been looking and trying different thing to synthesize rain noise like this: https://mynoise.net/NoiseMachines/campingRainNoiseGenerator.php but I cannot get it. and the graph that this sound makes did not help at all: can some make a block diagram of how to do this?
4. ### I Higher-Order Time Correlation Functions of White Noise?

Suppose I have Gaussian white noise, with the usual dirac-delta autocorrelation function, <F1(t1)F2(t2)> = s2*d(t1-t2)*D12 Where s is the standard deviation of the Gaussian, little d is the delta function, and big D is the kronecker delta. For concreteness and to keep track of units, say F...
5. ### I White noise & 1/f noise after a system h(t)

Hi, I am trying to solve this math equation on finding the variance of a noise after passing through a system whose impulse response is h(t) X is the input noise of the system and Y is the output noise after system h(t) if let's say variance of noise Y is σy2=∫∫Rxx(u,v)h(u)h(v)dudv where...
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### Studying Does white noise impair studying, reading or recall/memor?

Hi, I recently have been trying to look into whether or not white noise works as a means to block out external sounds so i can concentrate. However, I want to know whether it actually impairs studying and reading. I do not care if it has no benefit, as long as it has no negative effects. I am...
7. N

### Cross-correlation of white noise process with its conjugate

If w[n] are samples of the white gaussian noise process, I know that E[w[n1] w[n2]] = 0 for a WGN process. what would the following expression lead to: E[w[n1] w*[n2]] = ? Would it also be zero? Thanks a lot!
8. ### B Does the Amplitude of White Noise Double When Two Samples are Added Together?

Suppose you have two samples of white noise of equal amplitude. If you add them together ((sub)sample-by-(sub)sample that is), do you get one sample of white noise with twice the amplitude? How about pink noise?
9. ### Discretizing a Fluctuation Dissipation Theorem

Hey! I want to discretize a fluctuation dissipation theorem for the white noise ζ of a stochastic differential equation on a 2D domain (sphere). For that I integrate over "Finite Volume" elements with area A and A' (see below). \begin{eqnarray*} \int_{A} d A \int_{A'} d A'...
10. ### Simulating noise with Yuler and Burg

Hi After removing high frequency white noise in my INS sensor, I want to simulate low frequency noise with Burg or Yuler. I used some functions in python to analyse the recorded data and to get parameters to use. But the the problem is the sequences generated diverge (and take very big...
11. ### Thermal White Noise - Johnson–Nyquist noise

I'm trying to measure the thermal white noise generated by chemical batteries. So far I've measured the current noise, the voltage noise (V noise) and the bandwidth (delta v). From the equation below, I'm trying to solve the equation for the frequency. The problem is that there's an...
12. ### Sampling low pass filtered white noise

Homework Statement If we filter out ideal white noise using an ideal LPF of cutoff frequency W Hz and then sample it at F Hz , What are the conditions for different F so that the resulting discrete signal is correlated, uncorrelated , statistically independent and orthogonal etc? I would...
13. ### White noise energy vs. frequency components energy.

"White noise" energy vs. frequency components energy. White noise, I have learned that is a mixdure of all possible frequency components at the same time. All at the same levels. White noise can for example occour in resistors where an electric current flows through. If I filter it through...
14. ### White noise going through a Hilbert filter.

Now, assume I have a white noise, n(t)\tilde \ N(0,1), i.e gaussian with zero mean and variance 1, and it goes through a Hilbert filter, i.e we get: $$\hat{n}(t) = \int_{-\infty}^{\infty} \frac{1}{t-\tau} n(\tau) d\tau$$ I read that \hat{n} should be also a gaussian, because this is an...
15. ### Variance of White Noise: How Can It Have Infinite Power?

Hi, I have a pretty simple question which I thought I do not need to make a topic about, but Google is actually not helping, which is surprising. So here it goes: How can white noise have infinite power if its variance is finite? As far as I am aware, the following is always valid for a...
16. ### Kalman, White Noise, Sensor Specification, Discretization?

Hi. I have a few questions about sensor specifications and its implementation in a Kalman Filter and simulation of gyroscope/accelerometer output. Abbreviation used: d - discrete c - continuous Q1: From book: Aided Navigation - Farrell (you don't need the book to understand the...
17. ### Measuring the White Noise Produced by a Resistor

Hi all, I want to measure the white noise produced by a resistor in my circuit. In order to do this I did the following: 1. Ground the excitation voltage of the circuit and measure the white noise voltage produced by connecting the output of the circuit to a 8.5DVM 2. Subtract the Avg DC...
18. ### Filter White Noise: Designing FIR Moving Average Filter

I want to generate a Gaussian white noise as an input to a vibration exciter. Since, it does not follow the high frequencies I need to low pass filter the signal. I need to implement a filter which makes minimum distortion to my signal in terms of temporal correlation of the filtered signal and...
19. ### Hypothesis testing for multivariate processes(ljung box white noise test)

hi guys, I'm trying to understand how the critical value of Q-statistics is calculated in multivariate ljung-box test. or even more simply, in the univariate ljung-box test. initially i used MATLAB for hypothesis testing, MATLAB as an output furnishes the critical values, but the modules in...
20. ### Is Autocorrelation of White Noise Zero?

I am really new to this and so I am trying to understand some basic stuff here. Autocorrelation of a univariate white noise is 0. Am I correct?
21. ### What happens to gaussian white noise when derived in continuous time?

Hello, I've got a problem where a recording signal is a signal + gaussian white noise (quite classic). I derive this signal and while I know the theoretical result of the derivative of the noiseless signal, but I can't figure out what happens to the noise after the operation. So...
22. ### White noise vs Black body radiation

Hi all: I am confused about one question. When we detect signal from human brain using coil in Nuclear Magnetic Resonance, two source contribute noise to our signal. One is coil itself. The other is human brain. Why can we think the noise from human brain is white noise? Can we compare the...
23. ### Autocorrelation of white noise.

I'm stuck with an elementary thing, it must be something obvious but I can't see what's wrong. Here it goes. I was writing up some elementary course material for an instrumentation course, and wanted to quickly introduce "white noise". Now, the usual definition of white noise is something...
24. ### Understanding Noise Specification Units in Accelerometers and Gyros

hello, I am stuck at understanding the units of noise specification of accelerometers and gyros. I am referring to the datasheet of 3DM-GX1 which has accelerometers and gyro sensors. the pdf is .. http://www.microstrain.com/pdf/3DM-GX1%20Detailed%20Specs%20-%20Rev%201%20-%20070723.pdf...
25. ### White noise in communication channel

hi all - its been very long - hope everyone is well! just a data comms related question: When modelling a communication channel we normally include AWGN, that is, Additive white gaussian noise. Can anybody tell me why we use white noise in the model. I know it has a constant power...
26. ### What Does the -1.0 to 1.0 Range in a White Noise Graph Represent?

What is represented by the -1.0 to 1.0 range of this graph? Four thousandths of a second of white noise: http://upload.wikimedia.org/wikipedia/en/thumb/5/55/Whitenoise.png/350px-Whitenoise.png I am not sure what I am looking at. It's from: http://en.wikipedia.org/wiki/White_noise
27. ### White Noise Generator: How Does it Work?

Hi guys I'm currently working on a university experiment trying top create acoustic crystals. We're using a white noise generator to generate sounds at all frequencies. However I'm unsure exactly how a white noise generator creates the random signal. Can anyone explain how the an analogue...
28. ### K-Delta Function in Autocorrelation of Gaussian White Noise

hi, I would like to know why dirak-delta function is used in autocorrelation in a way that the following is true: <å(t)å(t')>=2Dä(t-t') where å(t)is Gaussian white noise and D is the strength of the noise. Dora