# Spectral Audio Signal ProcessingSpectrum Analysis of NoiseWhite Noise

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## White Noise

White noise may be defined as a sequence of uncorrelated random values, where correlation is defined in Appendix C and discussed further below. Perceptually, white noise is a wideband ``hiss'' in which all frequencies are equally likely. In Matlab or Octave, band-limited white noise can be generated using the rand or randn functions:

```y = randn(1,100); % 100 samples of Gaussian white noise
% with zero mean and unit variance

x = rand(1,100);  % 100 white noise samples,
%   uniform between 0 and 1.
xn = 2*(x-0.5);   % Make it uniform between -1 and +1
```
True white noise is obtained in the limit as the sampling rate goes to infinity and as time goes to plus and minus infinity. In other words, we never work with true white noise, but rather a finite time-segment from a white noise which has been band-limited to less than half the sampling rate and sampled.

In making white noise, it doesn't matter how the amplitude values are distributed probabilistically. That is, the relative probability of different amplitudes at any single sample instant does not affect whiteness, provided there is some zero-mean distribution of amplitude. It only matters that successive samples of the sequence are uncorrelated. This means that knowing some of the samples does not help at all in predicting other samples. Further discussion regarding white noise appears in §C.3.

Subsections
Previous: Spectral Characteristics of Noise
Next: Testing for White Noise

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About the Author: Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.