Everything about White Noise totally explained
White noise is a random
signal (or process) with a flat
power spectral density. In other words, the signal's power spectral density has equal power in any band, at any centre frequency, having a given bandwidth. White noise is considered analogous to
white light which contains all frequencies.
An infinite-bandwidth, white noise signal is purely a theoretical construction. By having power at all frequencies, the total power of such a signal is infinite. In practice, a signal can be "white" with a flat spectrum over a defined frequency band.
Statistical properties
The term white noise is also commonly applied to a noise signal in the spatial domain which has an
autocorrelation which can be represented by a
delta function over the relevant space dimensions. The signal is then "white" in the
spatial frequency domain (this is equally true for signals in the angular frequency domain, for example, the distribution of a signal across all angles in the night sky). The image to the right displays a finite length, discrete time realization of a white noise process generated from a computer.
Being uncorrelated in time does not, however, restrict the values a signal can take. Any distribution of values is possible (although it must have zero
DC component). For example, on
Linux white noise can be generated with the command
cat /dev/urandom > /dev/dsp, feeding the kernel random number generator (uniformly distributed integers between 0 and 255) into the digital signal processor. Even a binary signal which can only take on the values 1 or 0 will be white if the sequence of zeros and ones is statistically uncorrelated. Noise having a continuous distribution, such as a
normal distribution, can of course be white.
It is often incorrectly assumed that
Gaussian noise (for example, noise with a Gaussian amplitude distribution — see
normal distribution) is necessarily white noise. However, neither property implies the other. Gaussianity refers to the probability that the signal has a certain value at a certain instant, while the term 'white' refers to the way the signal power (taken over time) is distributed among frequencies.
We can therefore find Gaussian white noise, but also Poisson, Cauchy, etc. white noises. Thus, the two words "Gaussian" and "white" are often both specified in mathematical models of systems. Gaussian white noise is a good approximation of many real-world situations and generates mathematically tractable models. These models are used so frequently that the term
additive white Gaussian noise has a standard abbreviation:
AWGN. Gaussian white noise has the useful statistical property that its values are independent (see
Statistical independence).
White noise is the generalized mean-square derivative of the
Wiener process or
Brownian motion.
Applications
One use for white noise is in the field of
architectural acoustics. In order to dissemble distracting, undesirable noises in interior spaces, a low level of constant white noise is generated.
It is used by some emergency vehicle
sirens due to its ability to cut through background noise, which makes it easier to locate.
White noise is commonly used in the production of
electronic music, usually either directly or as an input for a filter to create other types of noise signal. It is used extensively in
audio synthesis, typically to recreate percussive instruments such as
cymbals which have high noise content in their frequency domain.
It is also used to generate
impulse responses. To set up the
EQ for a concert or other performance in a venue, a short burst of white or pink noise is sent through the PA system and monitored from various points in the venue so that the engineer can tell if the acoustics of the building naturally boost or cut any frequencies. The engineer can then adjust the overall EQ to ensure a balanced mix.
White noise can be used for frequency response testing of amplifiers and electronic filters.
It is sometimes used with a flat response microphone and an automatic equalizer. The idea is that the system will generate white noise and the microphone will pick up the white noise produced by the speakers. It will then automatically equalize each frequency band to get a flat response.
That system is used in professional level equipment, some high-end home stereo and some high-end car radios.
White noise is used as the basis of some
random number generators.
White noise can be used to disorient individuals prior to
interrogation and may be used as part of
sensory deprivation techniques.
White noise machines are sold as privacy enhancers and sleep aids and to mask
tinnitus. White noise CDs, when used with headphones, can aid concentration by blocking out irritating or distracting noises in a person's environment.
Mathematical definition
White random vector
A random vector
Note that this
power spectral density corresponds to a
delta function for the
covariance function of
.
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