| White Noise |
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| stochastic processes | |
| noise | |
| statistics | |
| data compression | |
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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, e.g. 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, 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 (i.e. noise with a Gaussian amplitude distribution — see Normal Distribution ) is necessarily white noise. However, neither property implies the other. Gaussianity refers to the way signal values are distributed, while the term 'white' refers to the shape of the flat power spectral density. (left) and white noise (right) on a FFT Spectrogram with linear frequency axis (vertical)]] 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 . 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 . COLORS OF NOISE See Also: Colors of noise There are also other "colors" of noise, the most commonly used being Pink , Brown and blue. 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 Siren s due to its ability to cut through background noise and its lack of echo, which makes it easier to locate. White noise has also been used in Electronic Music , where it is used either directly or as an input for a filter to create other types of noise signal. In this respect, it is the analog to the Violin in Classical Music . 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. He or she can then adjust the overall EQ to ensure a balanced mix.
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