White Noise

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Spectral Audio Signal Processing

Statistical Signal Processing

Sample Power Spectral Density

Making White Noise with Dice

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The Fourier Transform (FT) gives the (complex) spectrum of a continuous-time signal of any length. — Click for https://ccrma.stanford.edu/~jos/mdft/Fourier_Transform_FT_Inverse.html

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The impulse signal is the shortest pulse signal. For discrete time (digital) systems, the impulse is a 1 followed by zeros. In continuous time, the impulse is a narrow, unit-area pulse (ideally infinitely narrow). The impulse is typically denoted by the Greek delta symbol δ and is often called the 'Dirac delta function', after Paul Dirac who pioneered its use (in addition to being a lead contributor in the development of Quantum Mechanics). — Click for https://ccrma.stanford.edu/~jos/filters/Impulse_Response_Representation.html

In signal processing, noise is a random signal. Broadband noise contains energy over a wide range of frequencies. — Click for http://en.wikipedia.org/wiki/White_noise

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Noise (in signal processing) is a random signal. In the language of statistical signal processing, a noise signal is typically modeled as 'stochastic process', which is in turn defined as a sequence of random variables. — Click for https://ccrma.stanford.edu/~jos/sasp/What_Noise.html

White noise is a random signal in which all frequencies are equally present over time. It is analogous to white light which, as Isaac Newton first realized, consists of the superposition of all visible light frequencies. — Click for https://ccrma.stanford.edu/~jos/sasp/White_Noise.html

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Spectral Audio Signal Processing

Statistical Signal Processing

Sample Power Spectral Density

Making White Noise with Dice

White Noise

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

$\displaystyle E\{v(n)v(n+m)\} = \left\{\begin{array}{ll} \sigma_v^2, & m=0 \\ [5pt] 0, & m\neq 0 \\ \end{array} \right. \isdef \sigma_v^2 \delta(m) \protect$

(C.26)

where $E\{f(v)\}$ 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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``Spectral Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2011, ISBN 978-0-9745607-3-1.
Copyright © 2022-02-28 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA), Stanford University

White Noise

``Spectral Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2011, ISBN 978-0-9745607-3-1. Copyright © 2022-02-28 by Julius O. Smith III Center for Computer Research in Music and Acoustics (CCRMA), Stanford University

``Spectral Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2011, ISBN 978-0-9745607-3-1.
Copyright © 2022-02-28 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA), Stanford University