Pink noise

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Pink noise or 1/ƒ noise is a signal or process with a frequency spectrum such that the power spectral density is inversely proportional to the frequency. In pink noise, each octave carries an equal amount of noise power. The name arises from being intermediate between white noise (1/ƒ0) and red noise (1/ƒ2) which is commonly known as Brownian noise.

Within the scientific literature the term 1/ƒ noise is sometimes used a little more loosely to refer to any noise with a power spectral density of the form

where ƒ is frequency and 0 < α < 2, with α usually close to 1. These "1/ƒ-like" noises occur widely in nature and are a source of considerable interest in many fields.The distinction between the noises with α near 1 and those with a broad range of α approximately corresponds to a much more basic distinction. The former (narrow sense) generally come from condensed matter systems in quasi-equilibrium, as discussed below [1]. The latter (broader sense) generally correspond to wide range of non-equilibrium driven dynamical systems.

The term flicker noise is sometimes used to refer to 1/ƒ noise, although this is more properly applied only to its occurrence in electronic devices due to a direct current. Mandelbrot and Van Ness proposed the name fractional noise (sometimes since called fractal noise) to emphasise that the exponent of the spectrum could take non-integer values and be closely related to fractional Brownian motion, but the term is very rarely used.



There is equal energy in all octaves (or similar log bundles). In terms of power at a constant bandwidth, 1/ƒ noise falls off at 3 dB per octave. At high enough frequencies 1/ƒ noise is never dominant. (White noise is equal energy per hertz.)

The human auditory system, which processes frequencies in a roughly logarithmic fashion approximated by the Bark scale, does not perceive them with equal sensitivity; signals in the 2–4-kHz octave sound loudest, and the loudness of other frequencies drops increasingly, depending both on the distance from the peak-sensitivity area and on the level. However, humans still differentiate between white noise and pink noise with ease.

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