## Dr. Ahmed G. Abo-Khalil

Electrical Engineering Department

## White noise

In signal processing, white noise is a random signal with a flat (constant) power spectral density. In other words, a signal that contains equal power within any frequency band with a fixed width. The term is used, with this or similar meanings, in many scientific and technical disciplines, including physics, acoustic engineering, telecommunications, statistical forecasting, and many more. (Rigorously speaking, "white noise" refers to a statistical model for signals and signal sources, rather than to any specific signal.)

The term is also used for a discrete signal whose samples are regarded as a sequence of serially uncorrelated random variables with zero mean and finite variance. Depending on the context, one may also require that the samples be independent and have the same probability distribution. In particular, if each sample has a normal distribution with zero mean, the signal is said to be Gaussian white noise.[1] In digital image processing, the pixels of a white noise image are often assumed to be independent random variables with uniform distribution over some interval.

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, a random signal is considered "white noise" if it is observed to have a flat spectrum over the range of frequencies that is relevant to the context. For an audio signal, for example, the relevant range is the band of audible sound frequencies, between 20 to 20,000 Hz. Such a signal is heard as a hissing sound, resembling the /sh/ sound in "ash". In music and acoustics, the term white noise may be used for any signal that has a similar hissing sound.

White noise draws its name from white light, which is commonly (if incorrectly) assumed to have a flat power spectral density over the visible band.

The term is sometimes used in non technical contexts, in the metaphoric sense of "random talk without meaningful contents"

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