White Noise

Definition: To say that is a white noise means merely that successive samples are uncorrelated:

where denotes the expected value of (a function of the random variables ).

In other words, the autocorrelation function of white noise is an impulse at lag 0. Since the power spectral density is the Fourier transform of the autocorrelation function, the PSD of white noise is a constant. Therefore, all frequency components are equally present--hence the name ``white'' in analogy with white light (which consists of all colors in equal amounts).

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Subsections

• Making White Noise with Dice
• Independent Implies Uncorrelated
• Estimator Variance
  • Sample-Mean Variance
  • Sample-Variance Variance

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Next: Making White Noise with Dice

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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 Associate Professor (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.