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White noise

Properties and Characteristics of White Noise: – Any distribution of values is possible for white noise with a zero DC component. – A binary signal […]

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Properties and Characteristics of White Noise:
– Any distribution of values is possible for white noise with a zero DC component.
– A binary signal can be white if statistically uncorrelated.
– Gaussian noise does not imply white noise, as Gaussianity refers to amplitude distribution.
– White noise can be a derivative of the Wiener process or Brownian motion.
– White noise measure generalizes to random elements on infinite dimensional spaces.
– A white noise vector has components with zero mean and finite variance.
– Components of a white noise vector are statistically independent.
– The covariance matrix of a white noise vector is a diagonal matrix.
– Discrete-time white noise has a mean of zero for all instances.
– Autocorrelation function of white noise only has a nonzero value at lag 0.
– Pairwise correlations in white noise vectors are assumed to be zero.
– Gaussian white noise is often assumed for hypothesis testing and regression analysis.

Practical Applications of White Noise:
– Commonly used in electronic music production.
– Utilized to obtain the impulse response of electrical circuits.
– Basis for some random number generators.
– Used for sound masking in tinnitus treatment.
– Sold as privacy enhancers and sleep aids (white noise machines).
– Important in audio equipment testing and various electronic engineering applications.

White Noise in Music:
– Used in electronic music production to recreate percussive instruments.
– Extensively used in audio synthesis and as an input for filters.
– Commonly used in recreating static on nonexistent radio stations.
– White noise is a fundamental element in generating randomness in music.

White Noise in Electronics Engineering:
– Used to obtain impulse responses of electrical circuits.
– Crucial in audio equipment testing.
– Employed in various electronic engineering applications.
– Not suitable for testing loudspeakers due to high-frequency content.
– Pink noise is used for testing transducers like loudspeakers and microphones.

Computing and Tinnitus Treatment with White Noise:
– White noise serves as the basis for some random number generators.
– Used in computing for various applications.
– White noise is used for sound masking by tinnitus maskers.
– White noise machines are sold as privacy enhancers and sleep aids.
– FM radios tuned to unused frequencies can provide white noise for treatment.

White noise (Wikipedia)

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.

The waveform of a Gaussian white noise signal plotted on a graph
A "white noise" image

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.

Some "white noise" sound (very loud)

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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