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In science, Brownian noise, also known as Brown noise or red noise, is the type of signal noise produced by Brownian motion, hence its alternative name of random walk noise. The term "Brown noise" does not come from the color , but after Robert Brown , who documented the erratic motion for multiple types of inanimate particles in water.
Brownian noise, also called Brown noise, is noise with a power density which decreases 6.02 dB per octave (20 dB per decade) with increasing frequency (frequency density proportional to 1/f 2) over a frequency range excluding zero . It is also called "red noise", with pink being between red and white.
In applied mathematics, the Wiener process is used to represent the integral of a white noise Gaussian process, and so is useful as a model of noise in electronics engineering (see Brownian noise), instrument errors in filtering theory and disturbances in control theory. The Wiener process has applications throughout the mathematical sciences.
This observation is useful in defining Brownian motion on an m-dimensional Riemannian manifold (M, g): a Brownian motion on M is defined to be a diffusion on M whose characteristic operator in local coordinates x i, 1 ≤ i ≤ m, is given by 1 / 2 Δ LB, where Δ LB is the Laplace–Beltrami operator given in local coordinates by ...
The corresponding fluctuation is Brownian motion. An object in a fluid does not sit still, but rather moves around with a small and rapidly-changing velocity, as molecules in the fluid bump into it. Brownian motion converts heat energy into kinetic energy—the reverse of drag. Resistance and Johnson noise
White noise is commonly used in the production of electronic music, usually either directly or as an input for a filter to create other types of noise signal. It is used extensively in audio synthesis , typically to recreate percussive instruments such as cymbals or snare drums which have high noise content in their frequency domain. [ 8 ]
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Fractional Brownian motion has stationary increments X(t) = B H (s+t) − B H (s) (the value is the same for any s). The increment process X(t) is known as fractional Gaussian noise. There is also a generalization of fractional Brownian motion: n-th order fractional Brownian motion, abbreviated as n-fBm.