Төңкеріш дыбыс: Энергия теңдігі бар сигнал

Signal with equal energy per octave

[[File:2D pink noise. png|thumb|right|A two dimensional pink noise grayscale image, generated with a computer program. Some fields observed in nature are characterized by a similar power spectrum. It is often used to tune loudspeaker systems in professional audio. Pink noise is one of the most commonly observed signals in biological systems. The name arises from the pink appearance of visible light with this power spectrum. This is in contrast with white noise which has equal intensity per frequency interval.

[[File:White to pink filter. png|thumb|500px|The spatial filter which is convolved with a one dimensional white noise signal to create a pink noise signal

Unlike white noise, which has no correlations across the signal, a pink noise signal is correlated with itself, as follows.

The Pearson's correlation coefficient of a one dimensional pink noise signal (comprising discrete frequencies ) with itself across a distance in the configuration (space or time) domain is: see articles in Handel & Chung, 1993, and references therein). Examples of its occurrence include fluctuations in tide and river heights, quasar light emissions, heart beat, firings of single neurons, resistivity in solid state electronics and single molecule conductance signals resulting in flicker noise. Pink noise describes the statistical structure of many natural images. General 1/f α noises occur in many physical, biological and economic systems, and some researchers describe them as being ubiquitous. In physical systems, they are present in some meteorological data series, the electromagnetic radiation output of some astronomical bodies. In biological systems, they are present in, for example, heart beat rhythms, neural activity, and the statistics of DNA sequences, as a generalized pattern. An accessible introduction to the significance of pink noise is one given by Martin Gardner (1978) in his Scientific American column "Mathematical Games". In this column, Gardner asked for the sense in which music imitates nature. Sounds in nature are not musical in that they tend to be either too repetitive (bird song, insect noises) or too chaotic (ocean surf, wind in trees, and so forth). The answer to this question was given in a statistical sense by Voss and Clarke (1975, 1978), who showed that pitch and loudness fluctuations in speech and music are pink noises. So music is like tides not in terms of how tides sound, but in how tide heights vary.

In brains, pink noise has been widely observed across many temporal and physical scales from ion channel gating to EEG and MEG and LFP recordings in humans. In clinical EEG, deviations from this 1/f pink noise can be used to identify epilepsy, even in the absence of a seizure, or during the interictal state. Classic models of EEG generators suggested that dendritic inputs in gray matter were principally responsible for generating the 1/f power spectrum observed in EEG/MEG signals. However, recent computational models using cable theory have shown that action potential transduction along white matter tracts in the brain also generates a 1/f spectral density. Therefore, white matter signal transduction may also contribute to pink noise measured in scalp EEG recordings. It has also been successfully applied to the modeling of mental states in psychology, and used to explain stylistic variations in music from different cultures and historic periods. Richard F. Voss and J. Clarke claim that almost all musical melodies, when each successive note is plotted on a scale of pitches, will tend towards a pink noise spectrum. Similarly, a generally pink distribution pattern has been observed in film shot length by researcher James E. Cutting of Cornell University, in the study of 150 popular movies released from 1935 to 2005. Pink noise has also been found to be endemic in human response. Gilden et al. (1995) found extremely pure examples of this noise in the time series formed upon iterated production of temporal and spatial intervals. Later, Gilden (1997) and Gilden (2001) found that time series formed from reaction time measurement and from iterated two alternative forced choice also produced pink noises.

The principal sources of pink noise in electronic devices are almost invariably the slow fluctuations of properties of the condensed matter materials of the devices. In many cases the specific sources of the fluctuations are known. These include fluctuating configurations of defects in metals, fluctuating occupancies of traps in semiconductors, and fluctuating domain structures in magnetic materials. The explanation for the approximately pink spectral form turns out to be relatively trivial, usually coming from a distribution of kinetic activation energies of the fluctuating processes. Since the frequency range of the typical noise experiment (e. g., 1 Hz – 1 kHz) is low compared with typical microscopic "attempt frequencies" (e. g., 1014 Hz), the exponential factors in the Arrhenius equation for the rates are large. Relatively small spreads in the activation energies appearing in these exponents then result in large spreads of characteristic rates. In the simplest toy case, a flat distribution of activation energies gives exactly a pink spectrum, because

There is no known lower bound to background pink noise in electronics. Measurements made down to 10−6 Hz (taking several weeks) have not shown a ceasing of pink noise behaviour. (Kleinpenning, de Kuijper, 1988) measured the resistance in a noisy carbon sheet resistor, and found 1/f noise behavior over the range of , a range of 9.5 decades. A pioneering researcher in this field was Aldert van der Ziel. Flicker noise is commonly used for the reliability characterization of electronic devices. It is also used for gas detection in chemoresistive sensors by dedicated measurement setups.

1/f α noises with α near 1 are a factor in gravitational wave astronomy. The noise curve at very low frequencies affects pulsar timing arrays, the European Pulsar Timing Array (EPTA) and the future International Pulsar Timing Array (IPTA); at low frequencies are space borne detectors, the formerly proposed Laser Interferometer Space Antenna (LISA) and the currently proposed evolved Laser Interferometer Space Antenna (eLISA), and at high frequencies are ground based detectors, the initial Laser Interferometer Gravitational Wave Observatory (LIGO) and its advanced configuration (aLIGO). The characteristic strain of potential astrophysical sources are also shown. To be detectable the characteristic strain of a signal must be above the noise curve.

Pink noise on timescales of decades has been found in climate proxy data, which may indicate amplification and coupling of processes in the climate system.

Many time dependent stochastic processes are known to exhibit 1/f α noises with α between 0 and 2. In particular Brownian motion has a power spectral density that equals 4D/f 2, where D is the diffusion coefficient. This type of spectrum is sometimes referred to as Brownian noise. Interestingly, the analysis of individual Brownian motion trajectories also show 1/f 2 spectrum, albeit with random amplitudes. Fractional Brownian motion with Hurst exponent H also show 1/f α power spectral density with α=2H+1 for subdiffusive processes (H<0.5) and α=2 for superdiffusive processes (0.5<H<1).

There are many theories about the origin of pink noise. Some theories attempt to be universal, while others apply to only a certain type of material, such as semiconductors. Universal theories of pink noise remain a matter of current research interest. A hypothesis (referred to as the Tweedie hypothesis) has been proposed to explain the genesis of pink noise on the basis of a mathematical convergence theorem related to the central limit theorem of statistics. The Tweedie convergence theorem describes the convergence of certain statistical processes towards a family of statistical models known as the Tweedie distributions. These distributions are characterized by a variance to mean power law, that have been variously identified in the ecological literature as Taylor's law and in the physics literature as fluctuation scaling. When this variance to mean power law is demonstrated by the method of expanding enumerative bins this implies the presence of pink noise, and vice versa. There are various mathematical models to create pink noise. Although self organised criticality has been able to reproduce pink noise in sandpile models, these do not have a Gaussian distribution or other expected statistical qualities. It can be generated on computer, for example, by filtering white noise, inverse Fourier transform, or by multirate variants on standard white noise generation. an approximation free theory of stochastic differential equations, 1/f noise is one of the manifestations of the spontaneous breakdown of topological supersymmetry. This supersymmetry is an intrinsic property of all stochastic differential equations and its meaning is the preservation of the continuity of the phase space by continuous time dynamics. Spontaneous breakdown of this supersymmetry is the stochastic generalization of the concept of deterministic chaos, whereas the associated emergence of the long term dynamical memory or order, i. e., 1/f and crackling noises, the Butterfly effect etc., is the consequence of the Goldstone theorem in the application to the spontaneously broken topological supersymmetry.

Pink noise is commonly used to test the loudspeakers in sound reinforcement systems, with the resulting sound measured with a test microphone in the listening space connected to a spectrum analyzer Pink noise is still used by audio system contractors and by computerized sound systems which incorporate an automatic equalization feature. In manufacturing, pink noise is often used as a burn in signal for audio amplifiers and other components, to determine whether the component will maintain performance integrity during sustained use. The process of end users burning in their headphones with pink noise to attain higher fidelity has been called an audiophile "myth".