Understanding White Noise

 

 

    Understanding White Noise

   

  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 construct. 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 zero autocorrelation 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 below 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 correlations at two distinct times, which are independent of the noise amplitude distribution.

    We can therefore find Gaussian white noise, but also Poisson, Cauchy, etc. white noises. Note that the distribution must have infinite variance. 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.

 

 

 

 

 

 

    White Noise:

   White noise is a signal (or process) with a flat frequency spectrum in linear space. In other words, the signal has equal power in any linear band, at any center frequency, having a given bandwidth. For example, the 20 Hz frequency range between 40 and 60 Hz contains the same amount of power as the range between 4000 and 4020 Hz. An infinite-bandwidth white noise  signal is purely a theoretical construct. By having power at all frequencies, the total power of such a signal would be infinite. In practice, a signal is "white" if it has a flat spectrum over a defined frequency band.   

 

  

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