6170:
4944:
213:
1333:
6019:
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., 10 Hz), the exponential factors in the
997:
3133:
124:
1085:
1005:
923:
5441:
2842:
581:
4886:
671:
6085:
There is no known lower bound to background pink noise in electronics. Measurements made down to 10 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
3114:
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
1336:
The autocorrelation (Pearson's correlation coefficient) of one-dimensional (top) and two-dimensional (bottom) pink noise signals, across distance d (in units of the longest wavelength comprising the signal); grey curves are the autocorrelations of a sample of pink noise signals (comprising discrete
6447:
to obtain the desired results. Pink noise is predictable and repeatable, but it is annoying for a concert audience to hear. Since the late 1990s, FFT-based analysis enabled the engineer to make adjustments using pre-recorded music as the test signal, or even the music coming from the performers in
1056:
also divide signals into bands logarithmically and report power by octaves; audio engineers put pink noise through a system to test whether it has a flat frequency response in the spectrum of interest. Systems that do not have a flat response can be equalized by creating an inverse filter using a
6018:
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,
1092:
Pink noise can be computer-generated by first generating a white noise signal, Fourier-transforming it, then dividing the amplitudes of the different frequency components by the square root of the frequency (in one dimension), or by the frequency (in two dimensions) etc. This is equivalent to
5999:
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
4687:
3938:
112:
5170:
2681:
6023:
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
3718:
1057:
graphic equalizer. Because pink noise tends to occur in natural physical systems, it is often useful in audio production. Pink noise can be processed, filtered, and/or effects can be added to produce desired sounds. Pink-noise generators are commercially available.
396:
1538:, and the total power across all orientations, fall off as some power of the frequency. The following table lists these power-law frequency-dependencies for pink noise signal in different dimensions, and also for general power-law colored noise with power
5968:
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, particularly if the effects of ephaptic coupling are taken into consideration .
4183:
3006:
2618:
5743:
4692:
3115:
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.
3757:
3512:
The stability of the clock is measured by how many "ticks" it makes over a fixed interval. The more stable the number of ticks, the better the stability of the clock. So, define the average clock frequency over the interval
918:{\displaystyle h(x,y)={\frac {\sigma N}{\sqrt {2}}}\sum _{u,v}{\frac {\chi _{uv}}{\sqrt {u^{2}+v^{2}}}}\sin \left({\frac {2\pi }{N}}(ux+vy)+\phi _{uv}\right),\quad \chi _{uv}\sim \chi (2),\quad \phi _{uv}\sim U(0,2\pi ).}
5980:, 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
6337:. 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. Both of these effects can be shown to be the consequence of
4520:
6774:
4512:
6209:(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.
4014:
3566:
6081:
3051:
of an extraordinarily diverse number of physical and biological systems (Press, 1978; see articles in Handel & Chung, 1993, and references therein). Examples of its occurrence include fluctuations in
5163:
3445:
4295:
4026:
2453:
1337:
frequencies), and black is their average, red is the theoretically calculated autocorrelation when the signal comprises these same discrete frequencies, and blue assumes a continuum of frequencies
316:
5887:
5108:
5436:{\displaystyle \sigma ^{2}(\tau )\approx \int _{0}^{\infty }S(\omega )d\omega =\int _{0}^{\infty }S(\omega )\cdot S(\omega )d\omega =\int _{0}^{\infty }S(\tau \omega )\cdot S(\omega )d\omega }
2892:
8909:
Ovchinnikov, I.V.; Schwartz, R. N.; Wang, K. L. (2016). "Topological supersymmetry breaking: Definition and stochastic generalization of chaos and the limit of applicability of statistics".
2837:{\displaystyle r(d)={\frac {{\textrm {Ci}}({\frac {2\pi k_{\textrm {max}}d}{N}})-{\textrm {Ci}}({\frac {2\pi k_{\textrm {min}}d}{N}})}{\log {\frac {k_{\textrm {max}}}{k_{\textrm {min}}}}}},}
2514:
5630:
230:
6161:
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.
5516:
1312:
4934:
4439:
8416:
Krapf, Diego; Lukat, Nils; Marinari, Enzo; Metzler, Ralf; Oshanin, Gleb; Selhuber-Unkel, Christine; Squarcini, Alessio; Stadler, Lorenz; Weiss, Matthias; Xu, Xinran (2019-01-31).
2330:
5479:
576:{\displaystyle h(x)=\sigma {\sqrt {\frac {N}{2}}}\sum _{u}{\frac {\chi _{u}}{u}}\sin({\frac {2\pi ux}{N}}+\phi _{u}),\quad \chi _{u}\sim \chi (2),\quad \phi _{u}\sim U(0,2\pi ).}
5815:
1459:
1405:
2875:
2676:
2647:
2402:
229:
3507:
2234:
6313:
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
5779:
4980:
3354:
3318:
2273:
1672:
1634:
1371:
5555:
3282:
1741:
5911:
1516:
1489:
6763:
5038:
5655:
4881:{\displaystyle {\frac {1}{K}}\sum _{k=1}^{K}{\frac {1}{2}}(y_{k}-y_{k-1})^{2}\approx {\frac {1}{K\tau }}\int _{0}^{K\tau }{\frac {1}{2}}(g\ast {\dot {x}}_{f})(t)^{2}dt}
2079:
1947:
1586:
643:
609:
4327:
3087:
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
2380:
2187:
2115:
1983:
1869:
1556:
1536:
369:
4350:
5835:
5000:
3745:
3033:
1072:
capabilities because the signal power is a direct function of the crest factor. Various crest factors of pink noise can be used in simulations of various levels of
4379:
3244:
3195:
2422:
2360:
1703:
5916:
The cause of the noise floor is often traced to particular electronic components (such as transistors, resistors, and capacitors) within the oscillator feedback.
2144:
2012:
1898:
1833:
1799:
1770:
231:
9108:
7018:
Adak, Olgun; Rosenthal, Ethan; Meisner, Jeffery; Andrade, Erick F.; Pasupathy, Abhay N.; Nuckolls, Colin; Hybertsen, Mark S.; Venkataraman, Latha (2015-05-07).
5650:
3958:
3465:
3215:
2509:
2489:
2167:
2035:
1425:
1111:
666:
389:
345:
6149:
3561:
6306:
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
371:, which has been suitably filtered), as a sum of sine waves with different frequencies, whose amplitudes fall off inversely with the square root of frequency
6459:
and other components, to determine whether the component will maintain performance integrity during sustained use. The process of end-users burning in their
7704:
5837:, meaning that the clock frequency does not become more stable by simply averaging for longer. This contrasts with a white noise fluctuation, in which case
4016:, meaning that if the clock is used to repeatedly measure intervals of 7 hours, the standard deviation of the actually measured time would be around 40
7419:"5.4. Frequency and Time Standards††This work was supported in part by contract NSR 09-015-098 from the National Aeronautics and Space Administration."
6448:
real time. Pink noise is still used by audio system contractors and by computerized sound systems which incorporate an automatic equalization feature.
6205:(LISA) and the currently proposed evolved Laser Interferometer Space Antenna (eLISA), and at high frequencies are ground-based detectors, the initial
6391:. This supersymmetry is an intrinsic property of all stochastic differential equations and its meaning is the preservation of the continuity of the
2889:
The
Pearson's autocorrelation coefficient of a two-dimensional pink noise signal comprising discrete frequencies is theoretically approximated as:
8795:
4682:{\displaystyle \sigma ^{2}(\tau )={\frac {1}{2}}{\overline {(y_{k}-y_{k-1})^{2}}}={\frac {1}{2}}{\overline {(g\ast {\dot {x}}_{f})(k\tau )^{2}}}}
3933:{\displaystyle \sigma ^{2}(\tau )={\frac {1}{2}}{\overline {(y_{k}-y_{k-1})^{2}}}={\frac {1}{K}}\sum _{k=1}^{K}{\frac {1}{2}}(y_{k}-y_{k-1})^{2}}
264:
Within the scientific literature, the term 1/f noise is sometimes used loosely to refer to any noise with a power spectral density of the form
7548:
Douglas, PK; et al. (2019). "Reconsidering
Spatial Priors in EEG Source Estimation : Does White Matter Contribute to EEG Rhythms?".
7344:
Hinkley, N.; Sherman, J. A.; Phillips, N. B.; Schioppo, M.; Lemke, N. D.; Beloy, K.; Pizzocaro, M.; Oates, C. W.; Ludlow, A. D. (2013-09-13).
6217:
Pink noise on timescales of decades has been found in climate proxy data, which may indicate amplification and coupling of processes in the
5956:
were principally responsible for generating the 1/f power spectrum observed in EEG/MEG signals. However, recent computational models using
648:
In a two-dimensional pink noise signal, the amplitude at any orientation falls off inversely with frequency. A pink noise square of length
6376:
269:
4444:
9219:
6169:
324:
is frequency, and 0 < α < 2, with exponent α usually close to 1. One-dimensional signals with α = 1 are usually called pink noise.
3963:
6912:
Mandelbrot, Benoit B.; Wallis, James R. (1969). "Computer
Experiments with Fractional Gaussian Noises: Part 3, Mathematical Appendix".
931:-like noises occur widely in nature and are a source of considerable interest in many fields. Noises with α near 1 generally come from
7989:
6027:
77:
1373:
only for one-dimensional signals. For two-dimensional signals (e.g., images) the average power spectrum at any orientation falls as
10086:
9735:
5113:
3359:
9902:
9393:
1118:
9536:
9359:
7951:
Kleinpenning, T. G. M. & de
Kuijper, A. H. (1988). "Relation between variance and sample duration of 1/f Noise signals".
7662:
7575:
7470:
6856:
6743:
6395:
by continuous time dynamics. Spontaneous breakdown of this supersymmetry is the stochastic generalization of the concept of
4188:
2463:
Unlike white noise, which has no correlations across the signal, a pink noise signal is correlated with itself, as follows.
2427:
10239:
9014:
3713:{\displaystyle y_{k}={\frac {1}{\tau }}\int _{k\tau }^{(k+1)\tau }{\dot {x}}(t)dt={\frac {x((k+1)\tau )-x(k\tau )}{\tau }}}
5840:
5043:
3960:
is an integer large enough for the averaging to converge to a definite value. For example, a 2013 atomic clock achieved
10096:
6202:
119:
image, generated with a computer program; some fields observed in nature are characterized by a similar power spectrum
9978:
9892:
8971:
8333:
6669:
6198:
5560:
3036:
8152:
Smulko, Janusz; Scandurra, Graziella; Drozdowska, Katarzyna; Kwiatkowski, Andrzej; Ciofi, Carmine; Wen, He (2024).
6380:
1000:
Spectrum of a pink noise approximation on a log-log plot; power density falls off at 10 dB/decade of frequency
127:
A 3D pink noise image, generated with a computer program, viewed as an animation in which each frame is a 2D slice
10233:
10081:
9932:
9610:
8988:
7701:
6368:
or other expected statistical qualities. It can be generated on computer, for example, by filtering white noise,
5984:, will tend towards a pink noise spectrum. Similarly, a generally pink distribution pattern has been observed in
6301:
5484:
6321:
describes the convergence of certain statistical processes towards a family of statistical models known as the
4178:{\displaystyle y_{k}-y_{k-1}=\int _{\mathbb {R} }g(k\tau -t){\dot {x}}_{f}(t)dt=(g\ast {\dot {x}}_{f})(k\tau )}
2878:
2471:
The
Pearson's correlation coefficient of a one-dimensional pink noise signal (comprising discrete frequencies
391:(so that power, which is the square of amplitude, falls off inversely with frequency), and phases are random:
9766:
9560:
7599:
Douglas, PK; Blair, G.; et al. (2024). "Towards a white matter ephaptic coupling model of 1/f spectra".
1321:
1088:
The spatial filter which is convolved with a one-dimensional white noise signal to create a pink noise signal
197:
The name arises from the pink appearance of visible light with this power spectrum. This is in contrast with
70:
7146:
Gardner, M. (1978). "Mathematical Games—White and brown music, fractal curves and one-over-f fluctuations".
4891:
2620:
If instead of discrete frequencies, the pink noise comprises a superposition of continuous frequencies from
2342:
Consider pink noise of any dimension that is produced by generating a
Gaussian white noise signal with mean
10275:
10142:
10049:
9045:
6194:
6186:
4384:
7019:
3001:{\displaystyle r(d)={\frac {\sum _{k}{\frac {J_{0}({\frac {2\pi kd}{N}})}{k}}}{\sum _{k}{\frac {1}{k}}}},}
2279:
9897:
9619:
8594:
Eisler Z, Bartos I, Kertesz J (2008). "Fluctuation scaling in complex systems: Taylor's law and beyond".
8357:
Krapf, Diego; Marinari, Enzo; Metzler, Ralf; Oshanin, Gleb; Xu, Xinran; Squarcini, Alessio (2018-02-09).
8234:
6733:
6338:
6318:
6174:
5450:
1050:
for a given intensity. However, humans still differentiate between white noise and pink noise with ease.
156:
5784:
3747:
is unitless: it is the numerical ratio between ticks of the physical clock and ticks of an ideal clock.
2613:{\displaystyle r(d)={\frac {\sum _{k}{\frac {\cos {\frac {2\pi kd}{N}}}{k}}}{\sum _{k}{\frac {1}{k}}}}.}
1430:
1376:
9351:
9266:
Gisiger, T. (2001). "Scale invariance in biology: coincidence or footprint of a universal mechanism?".
7953:
6532:
6424:
6357:
6350:
6266:
2847:
2652:
2623:
2385:
957:
9583:
8806:
8647:
Kendal WS (2015). "Self-organized criticality attributed to a central limit-like convergence effect".
7418:
6345:
under the central limit theorem. This hypothesis also provides for an alternative paradigm to explain
5952:, or during the interictal state. Classic models of EEG generators suggested that dendritic inputs in
3470:
2193:
10244:
10192:
9822:
9715:
9181:
8154:"Flicker Noise in Resistive Gas Sensors—Measurement Setups and Applications for Enhanced Gas Sensing"
7916:
7875:
6517:
6369:
3129:
The ubiquitous 1/f noise poses a "noise floor" to precision timekeeping. The derivation is based on.
3092:
1073:
1027:
of frequency. The energy of pink noise at each frequency level, however, falls off at roughly 3
9241:
7830:
6599:
5748:
4949:
3323:
3287:
2240:
1641:
1603:
1349:
1046:, does not perceive different frequencies with equal sensitivity; signals around 1–4 kHz sound
9282:
8479:
7129:
Josephson, Brian D. (1995). "A trans-human source of music?" in (P. Pylkkänen and P. Pylkkö, eds.)
5944:
recordings in humans. In clinical EEG, deviations from this 1/f pink noise can be used to identify
5525:
3249:
3048:
1714:
932:
63:
7622:
Van Orden, G.C.; Holden, J.G.; Turvey, M.T. (2003). "Self-organization of cognitive performance".
6572:"Relations between the statistics of natural images and the response properties of cortical cells"
5738:{\displaystyle \sigma ^{2}(\tau )\approx \tau ^{\alpha -1}\sigma ^{2}(1)\propto \tau ^{\alpha -1}}
2382:, then multiplying its spectrum with a filter (equivalent to spatially filtering it with a filter
1093:
spatially filtering (convolving) the white noise signal with a white-to-pink-filter. For a length
10106:
9695:
9486:
9130:
7079:
6482:
6477:
5892:
5040:
shrinks on the x-axis, and the green curve shrinks on the x-axis but expands on the y-axis; when
3069:
1494:
1467:
9212:"Relations Between the Statistics of Natural Images and the Response Profiles of Cortical Cells"
8703:
O'Brien, Kevin P.; Weissman, M. B. (1992-10-01). "Statistical signatures of self-organization".
5005:
10029:
9964:
9927:
9277:
9236:
9061:
8359:"Power spectral density of a single Brownian trajectory: what one can and cannot learn from it"
7825:
6822:
Camouflage detection & signal discrimination: theory, methods & experiments (corrected)
6594:
6436:
5937:
4943:
2404:). Then the point values of the pink noise signal will also be normally distributed, with mean
2041:
1909:
1565:
1013:
621:
587:
168:
164:
9561:
Coloured Noise: Matlab toolbox to generate power-law coloured noise signals of any dimensions.
10218:
10063:
9907:
6875:; Van Ness, J. W. (1968). "Fractional Brownian motions, fractional noises and applications".
6365:
6314:
5973:
5941:
4304:
3095:
output of some astronomical bodies. In biological systems, they are present in, for example,
2365:
2172:
2085:
1953:
1839:
1541:
1521:
1065:
1039:
977:
939:, as discussed below. Noises with a broad range of α generally correspond to a wide range of
354:
8836:
6686:
4332:
10127:
9644:
9460:
9422:
9385:
9326:
9228:
9190:
9139:
9124:
Bak, P.; Tang, C.; Wiesenfeld, K. (1987). "Self-Organized
Criticality: An Explanation of 1/
8928:
8873:
8832:
8712:
8656:
8613:
8560:
8498:
8439:
8380:
8282:
8165:
8110:
8061:
8001:
7962:
7925:
7884:
7816:
7733:
7367:
7302:
7228:
7182:
7088:
7073:
Bak, P.; Tang, C.; Wiesenfeld, K. (1987). "Self-Organized
Criticality: An Explanation of 1/
7031:
6985:
6921:
6886:
6586:
6444:
6322:
5820:
4985:
3723:
3011:
1076:
in music signals. On some digital pink-noise generators the crest factor can be specified.
348:
176:
9521:
2007 IEEE International Conference on Acoustics, Speech and Signal Processing - ICASSP '07
8532:
Jørgensen B, Martinez JR, Tsao M (1994). "Asymptotic behaviour of the variance function".
8260:
4355:
3509:, meaning that on average, one second of clock-time passes for every second of real-time.
3220:
3171:
2407:
2345:
1679:
8:
9887:
9882:
9700:
9603:
9588:
7693:
6947:
6522:
6342:
6190:
6155:
2121:
1989:
1875:
1810:
1776:
1747:
238:
222:
9464:
9426:
9389:
9330:
9232:
9194:
9143:
8932:
8877:
8716:
8660:
8617:
8564:
8502:
8443:
8384:
8286:
8188:
8169:
8153:
8114:
8065:
8005:
7966:
7929:
7888:
7737:
7371:
7306:
7232:
7186:
7092:
7035:
7020:"Flicker Noise as a Probe of Electronic Interaction at Metal–Single Molecule Interfaces"
6989:
6925:
6890:
6590:
10285:
9943:
9833:
9542:
9503:
9451:
9413:
9303:
9268:
9211:
9163:
9093:
8944:
8918:
8891:
8863:
8683:
8629:
8603:
8576:
8429:
8370:
8328:. Karczub, D. G. (Denis G.) (2nd ed.). Cambridge, UK: Cambridge University Press.
8306:
8272:
8134:
8100:
7792:
7788:
7581:
7553:
7525:
7500:
7476:
7399:
7357:
7326:
7271:
7198:
7112:
6714:
6571:
6399:, whereas the associated emergence of the long-term dynamical memory or order, i.e., 1/
6020:
6004:
measurement and from iterated two-alternative forced choice also produced pink noises.
5993:
5889:, meaning that doubling the averaging time would improve the stability of frequency by
5635:
3943:
3450:
3200:
3157:
2494:
2474:
2152:
2020:
1410:
1096:
651:
374:
330:
191:
160:
91:
8073:
7430:
7345:
7159:
6089:
3516:
10157:
10152:
9948:
9772:
9669:
9654:
9634:
9532:
9515:
Chorti, A.; Brookes, M. (2007). "Resolving near-carrier spectral infinities due to 1/
9355:
9295:
9254:
9155:
8967:
8948:
8728:
8633:
8514:
8457:
8398:
8339:
8329:
8298:
8193:
8126:
8017:
7851:
7843:
7796:
7757:
7749:
7639:
7585:
7571:
7530:
7516:
7480:
7466:
7403:
7391:
7383:
7318:
7104:
7055:
7047:
6872:
6852:
6739:
6706:
6665:
6612:
6527:
6443:. The sound system plays pink noise while the audio engineer makes adjustments on an
6432:
6261:. Interestingly, the analysis of individual Brownian motion trajectories also show 1/
5985:
1316:
Matlab programs are available to generate pink and other power-law coloured noise in
1053:
961:
936:
179:
interval (halving or doubling in frequency) carries an equal amount of noise energy.
98:
9546:
9370:
9307:
8310:
8138:
7775:
Gilden, D. L. (1997). "Fluctuations in the time required for elementary decisions".
7462:
7275:
6718:
5928:, pink noise has been widely observed across many temporal and physical scales from
3754:
of the clock frequency is half the mean square of change in average clock frequency:
10250:
10223:
10197:
9777:
9710:
9674:
9524:
9495:
9468:
9430:
9334:
9287:
9246:
9198:
9167:
9147:
9022:
8936:
8895:
8881:
8746:
8720:
8664:
8621:
8580:
8568:
8506:
8447:
8388:
8294:
8290:
8183:
8173:
8118:
8069:
8009:
7970:
7933:
7892:
7835:
7784:
7741:
7679:
7631:
7608:
7604:
7563:
7520:
7512:
7458:
7426:
7375:
7330:
7310:
7263:
7236:
7202:
7190:
7155:
7116:
7096:
7039:
6929:
6894:
6826:
6698:
6630:
6604:
6408:
6254:
6238:
5989:
5961:
5444:
4937:
3077:
1042:, which processes frequencies in a roughly logarithmic fashion approximated by the
944:
615:
9507:
7450:
10228:
10182:
10147:
10137:
10015:
9705:
9664:
9442:
9404:
9317:
7708:
7567:
7043:
6820:
6497:
6456:
6412:
6404:
6330:
6310:. Universal theories of pink noise remain a matter of current research interest.
6234:
5443:
In words, the Allan variance is approximately the power of the fluctuation after
3217:. For concreteness, let us consider a quartz oscillator. In a quartz oscillator,
940:
194:. Pink noise is one of the most commonly observed signals in biological systems.
22:
9578:
8668:
8210:
8049:
7635:
6830:
1332:
10280:
9857:
9802:
9782:
9596:
9528:
9151:
8510:
8393:
8358:
7839:
7255:
7100:
6635:
6487:
6387:
noise is one of the manifestations of the spontaneous breakdown of topological
6270:
6258:
6218:
3751:
3124:
3107:
3088:
981:
245:
41:
9291:
9202:
8940:
8724:
8625:
8452:
8417:
7937:
7896:
10269:
10213:
10187:
9922:
9797:
9750:
9745:
9740:
9730:
9725:
9649:
9472:
9434:
8461:
8402:
8343:
8021:
7910:
Dutta, P. & Horn, P. M. (1981). "Low-frequency fluctuations in solids: 1/
7847:
7753:
7387:
7322:
7267:
7219:
Voss, R. F.; Clarke, J. (1978). "1/f noise" in music: Music from 1/f noise".
7051:
6542:
6512:
6388:
6307:
6013:
6001:
5981:
3284:
is the rate of oscillation. The rate of oscillation has a constant component
3106:
An accessible introduction to the significance of pink noise is one given by
3096:
3073:
952:
105:
9499:
8770:
7745:
7379:
6933:
6201:(IPTA); at low frequencies are space-borne detectors, the formerly proposed
4689:, and the discrete averaging can be approximated by a continuous averaging:
9912:
9862:
9792:
9299:
9250:
9159:
8908:
8518:
8302:
8197:
8130:
8122:
7855:
7643:
7601:
2024 12th International Winter Conference on Brain-Computer Interface (BCI)
7534:
7395:
7290:
7108:
7059:
6710:
6608:
6502:
6396:
5965:
5957:
3161:
3100:
1061:
46:
9338:
9258:
8732:
7761:
7550:
2019 7th International Winter Conference on Brain-Computer Interface (BCI)
6702:
6616:
6415:
in the application to the spontaneously broken topological supersymmetry.
9938:
9917:
9852:
9844:
9787:
9720:
9659:
8088:
6877:
6492:
6392:
5953:
5929:
4298:
4017:
3065:
1559:
1069:
1032:
1016:
1009:
198:
187:
31:
9315:
Johnson, J. B. (1925). "The Schottky effect in low frequency circuits".
9175:
Dutta, P.; Horn, P. M. (1981). "Low-frequency fluctuations in solids: 1/
8688:
6764:"Noise in Transistor Circuits: 1 - Mainly on fundamental noise concepts"
9839:
9812:
9807:
9639:
9409:"Über spontane Stromschwankungen in verschiedenen Elektrizitätsleitern"
7950:
7621:
6547:
6537:
6464:
6460:
6428:
5977:
3144:, as measured by the reference clock, the clock under test advances by
1084:
1043:
256:
51:
8886:
8851:
8178:
6329:, that have been variously identified in the ecological literature as
1461:. In every case, each octave carries an equal amount of noise power.
996:
10132:
9565:
8823:
Timmer, J.; König, M. (1995-01-01). "On Generating Power Law Noise".
8572:
8480:"Tweedie convergence: a mathematical basis for Taylor's power law, 1/
8211:
Moore, Christopher; Cole, Robert; Berry, Christopher (19 July 2013).
8013:
7990:"Relation between variance and sample duration of 1/ f noise signals"
7974:
7314:
7240:
7194:
6356:
There are various mathematical models to create pink noise. Although
6346:
6326:
3165:
3156:
Suppose that we have a timekeeping device (it could be anything from
1317:
183:
172:
116:
9446:
9408:
8212:
8151:
7873:
Noise and other slow non-exponential kinetics in condensed matter".
7719:
6898:
4507:{\displaystyle {\mathcal {F}}(\omega )={\mathcal {F}}(\tau \omega )}
1060:
One parameter of noise, the peak versus average energy contents, or
976:
noises for which the exponent α is not an even integer, or that are
8868:
8434:
8375:
8277:
7558:
7173:
Voss, R. F.; Clarke, J. (1975). "'1/f Noise' in Music and Speech".
6361:
5945:
1047:
1028:
8923:
8682:
Milotti, Edoardo (2002-04-12). "1/f noise: a pedagogical review".
8608:
8105:
8050:"Low-frequency noise study in electron devices: review and update"
7660:, International Semiotics Institute & University of Helsinki.
7362:
6976:
Press, W. H. (1978). "Flicker noises in astronomy and elsewhere".
6750:
Visible light with this power spectrum looks pink, hence the name.
4381:
be a packet of a square wave with height 1 and wavelength 2, then
4009:{\displaystyle \sigma (25000{\text{ seconds}})=1.6\times 10^{-18}}
123:
7133:, Finnish Artificial Intelligence Society, Helsinki; pp. 280–285.
6507:
6452:
5996:, in the study of 150 popular movies released from 1935 to 2005.
5949:
3132:
8261:"Intrinsic Pink-Noise Multidecadal Global Climate Dynamics Mode"
7425:, Astrophysics, vol. 12, Academic Press, pp. 198–227,
6871:
6229:
Many time-dependent stochastic processes are known to exhibit 1/
111:
9817:
9043:
Lacanette, Kerry (1990). "Create an Accurate Noise Generator".
6440:
6372:, or by multirate variants on standard white noise generation.
6076:{\displaystyle \textstyle {\frac {d}{df}}\ln f={\frac {1}{f}}.}
5925:
3061:
3057:
1024:
8259:
Moon, Woosok; Agarwal, Sahil; Wettlaufer, J. S. (2018-09-04).
7343:
6325:. These distributions are characterized by a variance to mean
10039:
10000:
9993:
9690:
7072:
6463:
with pink noise to attain higher fidelity has been called an
3152:
is the average (relative) clock frequency over that interval.
8531:
6341:
such as how certain kinds of data will converge towards the
1113:
signal in one dimension, the filter has the following form:
97:
This article is about 1/f noise. For quantum 1/f noise, see
8356:
7017:
6206:
5158:{\displaystyle \sigma ^{2}(\tau )\propto \tau ^{\alpha -1}}
3440:{\textstyle {\dot {x}}(t)={\dot {x}}_{0}+{\dot {x}}_{f}(t)}
3053:
242:
9618:
8326:
Fundamentals of noise and vibration analysis for engineers
7501:"Automated diagnosis of epilepsy using EEG power spectrum"
8415:
7002:
5972:
It has also been successfully applied to the modeling of
5933:
612:
8551:
Taylor LR (1961). "Aggregation, variance and the mean".
7988:
Kleinpenning, T. G. M.; de Kuijper, A. H. (1988-01-01).
6423:
Pink noise is commonly used to test the loudspeakers in
1004:
7417:
Vessot, Robert F. C. (1976-01-01), Meeks, M. L. (ed.),
6302:
Supersymmetry § Supersymmetry in dynamical systems
8852:"Introduction to supersymmetric theory of stochastics"
8418:"Spectral Content of a Single Non-Brownian Trajectory"
7987:
6288:<0.5) and α=2 for superdiffusive processes (0.5<
6031:
4982:
is approximately the area under the green curve; when
4290:{\displaystyle g(t)={\frac {-1_{}(t)+1_{}(t)}{\tau }}}
3362:
2448:{\displaystyle \lVert {\boldsymbol {a}}\rVert \sigma }
9096:
9090:
Though in practice, since there are no ideal clocks,
8258:
8086:
7218:
7172:
6092:
6030:
5895:
5843:
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5528:
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5116:
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5008:
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3726:
3569:
3519:
3473:
3453:
3326:
3290:
3252:
3223:
3203:
3174:
3136:
A clock is most easily tested by comparing it with a
3072:
and single-molecule conductance signals resulting in
3014:
2895:
2850:
2684:
2655:
2626:
2517:
2497:
2477:
2430:
2410:
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2368:
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1992:
1956:
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1121:
1099:
674:
654:
624:
590:
399:
377:
357:
333:
311:{\displaystyle S(f)\propto {\frac {1}{f^{\alpha }}},}
272:
9110:
is actually the ticks of a much more accurate clock.
7909:
7720:
Gilden, David L; Thornton, T; Mallon, MW (1995). "1/
7598:
6257:. This type of spectrum is sometimes referred to as
5882:{\displaystyle \sigma ^{2}(\tau )\propto \tau ^{-1}}
5103:{\displaystyle S(\omega )\propto \omega ^{-\alpha }}
9447:"Zur Berechnung und Beurteilung des Schroteffektes"
8702:
8593:
6207:
Laser Interferometer Gravitational-Wave Observatory
104:"Fractal noise" redirects here. For the novel, see
9102:
7810:Gilden, David L (2001). "Cognitive Emissions of 1/
7694:"Bringing New Understanding to the Director's Cut"
7291:"1/f noise with a low frequency white noise limit"
6189:. The noise curve at very low frequencies affects
6164:
6143:
6075:
5905:
5881:
5829:
5809:
5773:
5737:
5644:
5624:
5549:
5510:
5473:
5435:
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4177:
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3238:
3209:
3189:
3027:
3000:
2869:
2836:
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2641:
2612:
2503:
2483:
2447:
2416:
2396:
2374:
2354:
2324:
2267:
2228:
2181:
2161:
2138:
2109:
2073:
2029:
2006:
1977:
1941:
1892:
1863:
1827:
1793:
1764:
1735:
1697:
1666:
1628:
1580:
1550:
1530:
1510:
1483:
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1419:
1399:
1365:
1306:
1105:
917:
660:
637:
603:
575:
383:
363:
339:
310:
201:which has equal intensity per frequency interval.
9123:
8849:
7944:
1064:, is important for testing purposes, such as for
10267:
8235:"Think pink for a better view of climate change"
7005:Noise in Physical Systems and 1/"f" Fluctuations
6911:
6451:In manufacturing, pink noise is often used as a
6427:, with the resulting sound measured with a test
5745:. In particular, when the fluctuating component
3099:rhythms, neural activity, and the statistics of
2511:in the configuration (space or time) domain is:
1035:which has equal energy at all frequency levels.
8477:
7868:
7809:
7141:
7139:
3060:light emissions, heart beat, firings of single
2337:
8473:
8471:
7615:
7448:
7289:Schick, K. L.; Verveen, A. A. (October 1974).
5625:{\displaystyle S(\omega )=C/\omega ^{\alpha }}
9604:
9566:Powernoise: Matlab software for generating 1/
9514:
9345:
8323:
8089:"Low-frequency 1/f noise in graphene devices"
7862:
7774:
7288:
6971:
6969:
6967:
6865:
6846:
6814:
6233:noises with α between 0 and 2. In particular
1019:with the vertical axis being linear frequency
351:signal with zero mean and standard deviation
71:
7592:
7541:
7221:Journal of the Acoustical Society of America
7214:
7212:
7136:
6975:
6842:
6840:
6812:
6810:
6808:
6806:
6804:
6802:
6800:
6798:
6796:
6794:
6565:
6563:
6349:manifestations that have been attributed to
3140:reference clock. During an interval of time
3078:statistical structure of many natural images
2439:
2431:
1008:Relative intensity of pink noise (left) and
9523:. Vol. 3. pp. III–1005–III–1008.
9371:"Flicker noises in astronomy and elsewhere"
9348:Electronic Noise and Fluctuations in Solids
9220:Journal of the Optical Society of America A
8822:
8468:
8232:
7803:
7768:
7713:
7624:Journal of Experimental Psychology: General
7547:
7145:
6996:
6849:Electronic Noise and Fluctuations in Solids
9611:
9597:
8640:
8587:
8544:
8213:"Gravitational Wave Detectors and Sources"
7903:
7498:
7455:Encyclopedia of Computational Neuroscience
7260:33rd Annual Symposium on Frequency Control
7007:. New York: American Institute of Physics.
6964:
6825:(PhD). The University of Texas at Austin.
6725:
6659:
6154:A pioneering researcher in this field was
5511:{\displaystyle \Delta \omega \sim 1/\tau }
1518:of a pink noise signal at any orientation
347:one-dimensional pink noise signal (i.e. a
327:The following function describes a length
78:
64:
9281:
9240:
9174:
9042:
9015:"What is Pink Noise and What Does It Do?"
8922:
8885:
8867:
8747:"Noise in Man-generated Images and Sound"
8687:
8646:
8607:
8451:
8433:
8392:
8374:
8276:
8187:
8177:
8104:
7829:
7680:"Noise in Man-generated Images and Sound"
7672:
7557:
7524:
7492:
7457:, New York, NY: Springer, pp. 1–12,
7361:
7346:"An Atomic Clock with 10 –18 Instability"
7209:
7166:
6837:
6791:
6761:
6598:
6560:
6360:has been able to reproduce pink noise in
6265:spectrum, albeit with random amplitudes.
4888:, which is the total power of the signal
4068:
1307:{\displaystyle a(x)={\frac {1}{N}}\left.}
1023:In pink noise, there is equal energy per
956:in electronic devices. In their study of
9441:
9403:
8989:"Sound System Commissioning - Say What?"
8986:
8047:
7453:, in Jaeger, Dieter; Jung, Ranu (eds.),
7449:Destexhe, Alain; Bédard, Claude (2020),
7066:
6168:
4942:
3131:
3118:
1331:
1083:
1003:
995:
122:
110:
10087:Signal-to-interference-plus-noise ratio
9479:
9314:
9265:
8793:
8681:
7700:. Retrieved on March 3, 2010. See also
6684:
6655:
6653:
2435:
2390:
10268:
9903:Equivalent pulse code modulation noise
9059:
8550:
7416:
6731:
6431:in the listening space connected to a
6224:
5110:, the combined effect of both is that
4929:{\displaystyle (g\ast {\dot {x}}_{f})}
4441:, and its Fourier transform satisfies
3047:Pink noise has been discovered in the
2678:, the autocorrelation coefficient is:
9592:
9368:
9209:
7256:"1/F (Flicker) Noise: A Brief Review"
6569:
6185:noises with α near 1 are a factor in
6007:
5817:is independent of the averaging time
4434:{\displaystyle g(t)=h(t/\tau )/\tau }
10026:(energy per symbol to noise density)
9584:White Noise Definition Vs Pink Noise
9060:Thomas, Christian (April 30, 2021).
9049:. Vol. 38. Hayden. p. 108.
8961:
8796:"Numerical Simulation of Pink Noise"
7253:
7003:Handel, P. H.; Chung, A. L. (1993).
6687:"Pink-Noise Behaviour of Biosystems"
6650:
6377:supersymmetric theory of stochastics
3168:). Let its readout be a real number
2325:{\displaystyle 1/f^{1+(\alpha -1)d}}
1346:The power spectrum of pink noise is
1341:
7131:New Directions in Cognitive Science
6818:
6212:
5474:{\displaystyle \omega \sim 1/\tau }
3447:. By selecting the right units for
3246:is the number of oscillations, and
1031:per octave. This is in contrast to
175:of the signal. In pink noise, each
16:Signal with equal energy per octave
13:
10097:Signal-to-quantization-noise ratio
8534:Scandinavian Journal of Statistics
7789:10.1111/j.1467-9280.1997.tb00441.x
6762:Baxandall, P. J. (November 1968).
6660:Davis, Gary; Jones, Ralph (1987).
6435:or a computer running a real-time
6379:, an approximation-free theory of
6203:Laser Interferometer Space Antenna
6134:
6131:
6113:
6110:
5810:{\displaystyle \sigma ^{2}(\tau )}
5488:
5358:
5273:
5206:
4478:
4450:
3197:that changes with the actual time
2458:
1454:{\displaystyle {\frac {1}{f^{d}}}}
1400:{\displaystyle {\frac {1}{f^{2}}}}
211:
167:(power per frequency interval) is
90:For the album by Laura Mvula, see
14:
10297:
10011:(energy per bit to noise density)
9979:Carrier-to-receiver noise density
9893:Effective input noise temperature
9554:
8987:Eckstein, Matt (30 August 2018).
7160:10.1038/scientificamerican0478-16
6381:stochastic differential equations
6333:and in the physics literature as
6199:International Pulsar Timing Array
3037:Bessel function of the first kind
2870:{\displaystyle {\textrm {Ci}}(x)}
2671:{\displaystyle k_{\textrm {max}}}
2642:{\displaystyle k_{\textrm {min}}}
2397:{\displaystyle {\boldsymbol {a}}}
9622:(physics and telecommunications)
9399:from the original on 2007-09-27.
8478:Kendal WS, Jørgensen BR (2011).
7692:Anger, Natalie (March 1, 2010).
7517:10.1111/j.1528-1167.2012.03653.x
7499:Kerr, W.T.; et al. (2012).
6662:The Sound Reinforcement Handbook
6418:
6411:etc., is the consequence of the
6173:Noise curves for a selection of
3502:{\displaystyle {\dot {x}}_{0}=1}
2491:) with itself across a distance
2229:{\displaystyle 1/f^{\alpha d/2}}
1592:Power-law spectra of pink noise
255:Problems playing this file? See
227:
10234:Block-matching and 3D filtering
10082:Signal-to-noise ratio (imaging)
9933:Noise, vibration, and harshness
9084:
9053:
9036:
9012:
9006:
8980:
8966:. Routledge. pp. 274–276.
8955:
8902:
8843:
8816:
8787:
8763:
8739:
8696:
8675:
8525:
8409:
8350:
8317:
8252:
8226:
8204:
8145:
8080:
8041:
8028:
7981:
7686:
7650:
7463:10.1007/978-1-4614-7320-6_548-2
7442:
7423:Methods in Experimental Physics
7410:
7337:
7282:
7247:
7123:
7011:
6940:
6905:
6780:from the original on 2016-04-23
6439:(FFT) analyzer program such as
6284:+1 for subdiffusive processes (
6280:power spectral density with α=2
6165:In gravitational wave astronomy
964:and Van Ness proposed the name
874:
842:
535:
506:
9062:"Headphone burn-in isn't real"
8964:The Sound System Design Primer
8771:"DSP Generation of Pink Noise"
8295:10.1103/PhysRevLett.121.108701
8087:Alexander A. Balandin (2013).
7609:10.1109/BCI60775.2024.10480498
6755:
6738:. O'Reilly Media. p. 79.
6678:
6623:
6138:
6093:
5860:
5854:
5804:
5798:
5774:{\displaystyle {\dot {x}}_{f}}
5713:
5707:
5675:
5669:
5598:
5592:
5589:
5567:
5424:
5418:
5415:
5393:
5384:
5375:
5372:
5366:
5336:
5330:
5327:
5305:
5296:
5290:
5287:
5281:
5251:
5245:
5242:
5214:
5190:
5184:
5133:
5127:
5081:
5075:
5072:
5050:
5027:
5021:
5018:
5012:
4975:{\displaystyle \sigma ^{2}(1)}
4969:
4963:
4923:
4895:
4863:
4856:
4853:
4825:
4770:
4737:
4664:
4654:
4651:
4623:
4592:
4559:
4540:
4534:
4501:
4492:
4489:
4483:
4470:
4464:
4461:
4455:
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4406:
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4391:
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4267:
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4114:
4092:
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3692:
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3662:
3644:
3638:
3618:
3606:
3550:
3544:
3532:
3520:
3434:
3428:
3381:
3375:
3349:{\displaystyle {\dot {x}}_{f}}
3313:{\displaystyle {\dot {x}}_{0}}
3271:
3265:
3233:
3227:
3184:
3178:
2961:
2937:
2905:
2899:
2864:
2858:
2789:
2756:
2743:
2710:
2694:
2688:
2527:
2521:
2314:
2302:
2268:{\displaystyle 1/f^{\alpha d}}
1692:
1686:
1667:{\displaystyle p_{\theta }(f)}
1661:
1655:
1629:{\displaystyle a_{\theta }(f)}
1623:
1617:
1366:{\displaystyle {\frac {1}{f}}}
1292:
1280:
1199:
1187:
1131:
1125:
991:
909:
894:
868:
862:
815:
797:
690:
678:
567:
552:
529:
523:
500:
463:
409:
403:
282:
276:
1:
9767:Additive white Gaussian noise
9519:phase noise in oscillators".
9117:
8074:10.1016/S0026-2714(02)00347-5
8034:Aldert van der Ziel, (1954),
7451:"Local Field Potentials: LFP"
7431:10.1016/S0076-695X(08)60710-3
5550:{\displaystyle 1/f^{\alpha }}
3277:{\displaystyle {\dot {x}}(t)}
3042:
1736:{\displaystyle 1/{\sqrt {f}}}
1327:
1079:
204:
115:A two-dimensional pink noise
10143:Interference (communication)
10050:Signal-to-interference ratio
10040:Signal, noise and distortion
9570:noise, or more generally, 1/
8054:Microelectronics Reliability
7663:"On Musical Self-Similarity"
7568:10.1109/IWW-BCI.2019.8737307
7044:10.1021/acs.nanolett.5b01270
6664:. Hal Leonard. p. 107.
6554:
6364:models, these do not have a
6195:European Pulsar Timing Array
6187:gravitational-wave astronomy
6175:gravitational-wave detectors
4674:
4602:
3839:
3320:and a fluctuating component
3103:, as a generalized pattern.
2884:
2466:
2338:Distribution of point values
7:
9898:Equivalent noise resistance
8794:McClain, D. (May 1, 2001).
8669:10.1016/j.physa.2014.11.035
7869:Weissman, M. B. (1988). "1/
7724:Noise in Human Cognition".
7636:10.1037/0096-3445.132.3.331
6831:10.13140/RG.2.2.10585.80487
6691:European Biophysics Journal
6470:
6425:sound reinforcement systems
6319:Tweedie convergence theorem
5948:, even in the absence of a
5906:{\displaystyle {\sqrt {2}}}
4517:The Allan variance is then
3076:. Pink noise describes the
1511:{\displaystyle p_{\theta }}
1484:{\displaystyle a_{\theta }}
950:Pink noise sources include
186:. It is often used to tune
10:
10302:
9529:10.1109/ICASSP.2007.366852
9480:Keshner, M. S. (1982). "1/
9352:Cambridge University Press
9152:10.1103/PhysRevLett.59.381
8850:Ovchinnikov, I.V. (2016).
8825:Astronomy and Astrophysics
8511:10.1103/physreve.84.066120
8484:noise and multifractality"
8233:Jim Shelton (2018-09-04).
7994:Journal of Applied Physics
7954:Journal of Applied Physics
7840:10.1037/0033-295X.108.1.33
7658:On Musical Self-Similarity
7101:10.1103/PhysRevLett.59.381
6533:Self-organised criticality
6358:self-organised criticality
6351:self-organized criticality
6299:
6267:Fractional Brownian motion
6177:as a function of frequency
6151:, a range of 9.5 decades.
6011:
5033:{\displaystyle S(\omega )}
3122:
958:fractional Brownian motion
237:10 seconds of pink noise,
103:
96:
89:
10206:
10193:Total variation denoising
10175:
10166:
10120:
9957:
9873:
9759:
9683:
9627:
9579:1/f noise at Scholarpedia
9292:10.1017/S1464793101005607
9203:10.1103/RevModPhys.53.497
9182:Reviews of Modern Physics
8941:10.1142/S021798491650086X
8725:10.1103/PhysRevA.46.R4475
8626:10.1080/00018730801893043
8453:10.1103/PhysRevX.9.011019
7938:10.1103/RevModPhys.53.497
7917:Reviews of Modern Physics
7897:10.1103/RevModPhys.60.537
7876:Reviews of Modern Physics
6370:inverse Fourier transform
6295:
5919:
4936:, or the integral of its
3093:electromagnetic radiation
2074:{\displaystyle 1/f^{d/2}}
1942:{\displaystyle 1/f^{3/2}}
1581:{\displaystyle \alpha =2}
1074:dynamic range compression
638:{\displaystyle \phi _{u}}
616:chi-distributed variables
604:{\displaystyle \chi _{u}}
182:Pink noise sounds like a
9473:10.1002/andp.19223731007
9435:10.1002/andp.19183622304
9378:Comments on Astrophysics
8911:Modern Physics Letters B
8394:10.1088/1367-2630/aaa67c
7268:10.1109/FREQ.1979.200297
6978:Comments in Astrophysics
6914:Water Resources Research
6339:mathematical convergence
3049:statistical fluctuations
2879:cosine integral function
1427:dimensions, it falls as
968:(sometimes since called
10107:Contrast-to-noise ratio
9500:10.1109/PROC.1982.12282
9487:Proceedings of the IEEE
9131:Physical Review Letters
8837:1995A&A...300..707T
8265:Physical Review Letters
7746:10.1126/science.7892611
7552:. IEEE. pp. 1–12.
7380:10.1126/science.1240420
7254:Voss, R.F. (May 1979).
7080:Physical Review Letters
6934:10.1029/WR005i001p00260
6483:Audio signal processing
6478:Architectural acoustics
4322:{\displaystyle 1/\tau }
3070:solid-state electronics
2375:{\displaystyle \sigma }
2182:{\displaystyle \alpha }
2110:{\displaystyle 1/f^{d}}
1978:{\displaystyle 1/f^{3}}
1864:{\displaystyle 1/f^{2}}
1551:{\displaystyle \alpha }
1531:{\displaystyle \theta }
364:{\displaystyle \sigma }
10030:Modulation error ratio
9965:Carrier-to-noise ratio
9928:Noise spectral density
9346:Kogan, Shulim (1996).
9251:10.1364/JOSAA.4.002379
9104:
8363:New Journal of Physics
8324:Norton, M. P. (2003).
8123:10.1038/nnano.2013.144
7603:. IEEE. pp. 1–3.
6847:Kogan, Shulim (1996).
6819:Das, Abhranil (2022).
6732:Downey, Allen (2012).
6631:"Glossary: Pink Noise"
6609:10.1364/JOSAA.4.002379
6437:fast Fourier transform
6239:power spectral density
6197:(EPTA) and the future
6178:
6145:
6077:
5907:
5883:
5831:
5811:
5775:
5739:
5646:
5626:
5551:
5512:
5475:
5437:
5165:
5159:
5104:
5034:
4996:
4976:
4930:
4882:
4726:
4683:
4508:
4435:
4375:
4346:
4345:{\displaystyle 2\tau }
4323:
4291:
4179:
4010:
3954:
3934:
3877:
3741:
3714:
3557:
3503:
3461:
3441:
3350:
3314:
3278:
3240:
3211:
3191:
3153:
3029:
3002:
2871:
2838:
2672:
2643:
2614:
2505:
2485:
2449:
2418:
2398:
2376:
2356:
2326:
2269:
2230:
2183:
2163:
2140:
2111:
2075:
2031:
2008:
1979:
1943:
1894:
1865:
1829:
1795:
1766:
1737:
1699:
1668:
1630:
1582:
1552:
1532:
1512:
1485:
1464:The average amplitude
1455:
1421:
1401:
1367:
1338:
1308:
1242:
1107:
1089:
1020:
1001:
978:fractional derivatives
919:
662:
639:
605:
577:
385:
365:
341:
312:
216:
169:inversely proportional
165:power spectral density
128:
120:
10245:Denoising autoencoder
10219:Anisotropic diffusion
10064:Signal-to-noise ratio
9908:Impulse noise (audio)
9823:Johnson–Nyquist noise
9711:Government regulation
9369:Press, W. H. (1978).
9339:10.1103/PhysRev.26.71
9210:Field, D. J. (1987).
9105:
8093:Nature Nanotechnology
7777:Psychological Science
6703:10.1007/s002490100143
6570:Field, D. J. (1987).
6518:Johnson–Nyquist noise
6366:Gaussian distribution
6323:Tweedie distributions
6315:central limit theorem
6255:diffusion coefficient
6172:
6146:
6078:
5988:length by researcher
5908:
5884:
5832:
5830:{\displaystyle \tau }
5812:
5781:is a 1/f noise, then
5776:
5740:
5647:
5627:
5557:fluctuation, we have
5552:
5513:
5476:
5438:
5160:
5105:
5035:
4997:
4995:{\displaystyle \tau }
4977:
4946:
4931:
4883:
4706:
4684:
4509:
4436:
4376:
4347:
4324:
4292:
4180:
4011:
3955:
3935:
3857:
3742:
3740:{\displaystyle y_{k}}
3715:
3558:
3504:
3462:
3442:
3351:
3315:
3279:
3241:
3212:
3192:
3135:
3119:Precision timekeeping
3030:
3028:{\displaystyle J_{0}}
3003:
2872:
2839:
2673:
2644:
2615:
2506:
2486:
2450:
2419:
2399:
2377:
2357:
2327:
2270:
2231:
2184:
2164:
2141:
2112:
2076:
2032:
2009:
1980:
1944:
1895:
1866:
1830:
1796:
1767:
1738:
1700:
1669:
1631:
1583:
1553:
1533:
1513:
1486:
1456:
1422:
1402:
1368:
1335:
1309:
1208:
1108:
1087:
1066:audio power amplifier
1040:human auditory system
1007:
999:
920:
663:
640:
606:
578:
386:
366:
342:
313:
215:
126:
114:
10128:List of noise topics
9094:
7817:Psychological Review
7656:Pareyon, G. (2011).
6773:. pp. 388–392.
6191:pulsar timing arrays
6090:
6028:
5893:
5841:
5821:
5785:
5749:
5656:
5636:
5561:
5526:
5485:
5451:
5171:
5114:
5044:
5006:
4986:
4950:
4892:
4693:
4521:
4445:
4385:
4374:{\displaystyle h(t)}
4356:
4333:
4305:
4189:
4027:
3964:
3944:
3758:
3724:
3567:
3517:
3471:
3451:
3360:
3324:
3288:
3250:
3239:{\displaystyle x(t)}
3221:
3201:
3190:{\displaystyle x(t)}
3172:
3012:
2893:
2848:
2682:
2653:
2624:
2515:
2495:
2475:
2428:
2417:{\displaystyle \mu }
2408:
2386:
2366:
2355:{\displaystyle \mu }
2346:
2280:
2241:
2194:
2173:
2153:
2122:
2086:
2042:
2021:
1990:
1954:
1910:
1876:
1840:
1811:
1777:
1748:
1715:
1698:{\displaystyle p(f)}
1680:
1642:
1604:
1566:
1542:
1522:
1495:
1468:
1431:
1411:
1377:
1350:
1119:
1097:
672:
652:
645:are uniform random.
622:
588:
397:
375:
355:
349:Gaussian white noise
331:
270:
10276:Noise (electronics)
9888:Circuit noise level
9883:Channel noise level
9465:1922AnP...373..157S
9427:1918AnP...362..541S
9390:1978ComAp...7..103P
9331:1925PhRv...26...71J
9233:1987JOSAA...4.2379F
9195:1981RvMP...53..497D
9144:1987PhRvL..59..381B
8962:Loar, Josh (2019).
8933:2016MPLB...3050086O
8878:2016Entrp..18..108O
8717:1992PhRvA..46.4475O
8661:2015PhyA..421..141K
8618:2008AdPhy..57...89E
8596:Advances in Physics
8565:1961Natur.189..732T
8503:2011PhRvE..84f6120K
8444:2019PhRvX...9a1019K
8385:2018NJPh...20b3029K
8287:2018PhRvL.121j8701M
8170:2024Senso..24..405S
8115:2013NatNa...8..549B
8066:2003MiRe...43..585W
8006:1988JAP....63...43K
7967:1988JAP....63...43K
7930:1981RvMP...53..497D
7889:1988RvMP...60..537W
7738:1995Sci...267.1837G
7732:(5205): 1837–1839.
7372:2013Sci...341.1215H
7356:(6151): 1215–1218.
7307:1974Natur.251..599S
7233:1978ASAJ...63..258V
7187:1975Natur.258..317V
7148:Scientific American
7093:1987PhRvL..59..381B
7036:2015NanoL..15.4143A
6990:1978ComAp...7..103P
6926:1969WRR.....5..260M
6891:1968SIAMR..10..422M
6685:Szendro, P (2001).
6591:1987JOSAA...4.2379F
6523:Noise (electronics)
6397:deterministic chaos
6343:normal distribution
6335:fluctuation scaling
6317:of statistics. The
6225:Diffusion processes
6156:Aldert van der Ziel
5964:transduction along
5362:
5277:
5210:
4814:
4297:is one packet of a
3625:
3112:Scientific American
3056:and river heights,
2139:{\displaystyle 1/f}
2007:{\displaystyle 1/f}
1893:{\displaystyle 1/f}
1828:{\displaystyle 1/f}
1794:{\displaystyle 1/f}
1765:{\displaystyle 1/f}
1593:
668:can be written as:
9944:Pseudorandom noise
9834:Quantization error
9645:Noise cancellation
9452:Annalen der Physik
9414:Annalen der Physik
9269:Biological Reviews
9100:
8775:www.firstpr.com.au
8711:(8): R4475–R4478.
7707:2013-01-24 at the
7698:The New York Times
7262:. pp. 40–46.
6579:J. Opt. Soc. Am. A
6179:
6141:
6086:over the range of
6073:
6072:
6021:Arrhenius equation
6008:Electronic devices
5994:Cornell University
5903:
5879:
5827:
5807:
5771:
5735:
5642:
5632:for some constant
5622:
5547:
5508:
5471:
5445:bandpass filtering
5433:
5348:
5263:
5196:
5166:
5155:
5100:
5030:
4992:
4972:
4926:
4878:
4797:
4679:
4504:
4431:
4371:
4342:
4319:
4287:
4175:
4006:
3950:
3930:
3737:
3710:
3593:
3553:
3499:
3457:
3437:
3346:
3310:
3274:
3236:
3207:
3187:
3158:quartz oscillators
3154:
3025:
2998:
2981:
2923:
2867:
2834:
2668:
2639:
2610:
2593:
2545:
2501:
2481:
2445:
2414:
2394:
2372:
2352:
2322:
2265:
2226:
2179:
2159:
2136:
2107:
2071:
2027:
2004:
1975:
1939:
1890:
1861:
1825:
1791:
1762:
1733:
1695:
1664:
1626:
1591:
1578:
1548:
1528:
1508:
1481:
1451:
1417:
1397:
1363:
1339:
1304:
1103:
1090:
1054:Graphic equalizers
1021:
1002:
915:
728:
658:
635:
601:
573:
439:
381:
361:
337:
308:
217:
192:professional audio
161:frequency spectrum
159:or process with a
129:
121:
92:Pink Noise (album)
10263:
10262:
10259:
10258:
10198:Wavelet denoising
10158:Thermal radiation
10153:Spectrum analyzer
9949:Statistical noise
9773:Atmospheric noise
9670:Noise temperature
9655:Noise measurement
9635:Acoustic quieting
9538:978-1-4244-0727-9
9361:978-0-521-46034-7
9227:(12): 2379–2394.
9103:{\displaystyle t}
9046:Electronic Design
8887:10.3390/e18040108
8705:Physical Review A
8559:(4766): 732–735.
8422:Physical Review X
8179:10.3390/s24020405
8048:Hei Wong (2003).
7577:978-1-5386-8116-9
7511:(11): e189–e192.
7472:978-1-4614-7320-6
7301:(5476): 599–601.
7181:(5533): 317–318.
6873:Mandelbrot, B. B.
6858:978-0-521-46034-7
6745:978-1-4493-1463-7
6585:(12): 2379–2394.
6528:Quantum 1/f noise
6433:spectrum analyzer
6413:Goldstone theorem
6067:
6045:
5901:
5762:
5645:{\displaystyle C}
5580:
5406:
5318:
5233:
5063:
4914:
4844:
4823:
4795:
4735:
4704:
4677:
4642:
4618:
4605:
4554:
4285:
4151:
4105:
3979:
3953:{\displaystyle K}
3886:
3855:
3842:
3791:
3708:
3635:
3591:
3484:
3460:{\displaystyle x}
3419:
3397:
3372:
3337:
3301:
3262:
3210:{\displaystyle t}
3138:far more accurate
3091:data series, the
2993:
2990:
2972:
2968:
2959:
2914:
2855:
2829:
2826:
2822:
2810:
2787:
2776:
2753:
2741:
2730:
2707:
2664:
2635:
2605:
2602:
2584:
2580:
2574:
2536:
2504:{\displaystyle d}
2484:{\displaystyle k}
2335:
2334:
2162:{\displaystyle d}
2030:{\displaystyle d}
1731:
1449:
1420:{\displaystyle d}
1395:
1361:
1342:Power-law spectra
1278:
1253:
1252:
1176:
1175:
1145:
1106:{\displaystyle N}
945:dynamical systems
937:quasi-equilibrium
795:
769:
768:
713:
711:
710:
661:{\displaystyle N}
485:
455:
430:
428:
427:
384:{\displaystyle u}
340:{\displaystyle N}
303:
232:
99:quantum 1/f noise
88:
87:
10293:
10251:Deep Image Prior
10240:Shrinkage Fields
10224:Bilateral filter
10173:
10172:
9778:Background noise
9675:Phase distortion
9613:
9606:
9599:
9590:
9589:
9550:
9511:
9476:
9438:
9400:
9398:
9375:
9365:
9342:
9311:
9285:
9262:
9244:
9216:
9206:
9171:
9111:
9109:
9107:
9106:
9101:
9088:
9077:
9076:
9074:
9072:
9057:
9051:
9050:
9040:
9034:
9033:
9031:
9029:
9023:Yamaha Pro Audio
9010:
9004:
9003:
9001:
8999:
8984:
8978:
8977:
8959:
8953:
8952:
8926:
8906:
8900:
8899:
8889:
8871:
8847:
8841:
8840:
8820:
8814:
8813:
8811:
8805:. Archived from
8800:
8791:
8785:
8784:
8782:
8781:
8767:
8761:
8760:
8758:
8757:
8743:
8737:
8736:
8700:
8694:
8693:
8691:
8679:
8673:
8672:
8644:
8638:
8637:
8611:
8591:
8585:
8584:
8573:10.1038/189732a0
8548:
8542:
8541:
8529:
8523:
8522:
8488:
8475:
8466:
8465:
8455:
8437:
8413:
8407:
8406:
8396:
8378:
8354:
8348:
8347:
8321:
8315:
8314:
8280:
8256:
8250:
8249:
8247:
8245:
8230:
8224:
8223:
8221:
8219:
8208:
8202:
8201:
8191:
8181:
8149:
8143:
8142:
8108:
8084:
8078:
8077:
8045:
8039:
8032:
8026:
8025:
8014:10.1063/1.340460
7985:
7979:
7978:
7975:10.1063/1.340460
7948:
7942:
7941:
7907:
7901:
7900:
7866:
7860:
7859:
7833:
7807:
7801:
7800:
7772:
7766:
7765:
7717:
7711:
7690:
7684:
7683:
7676:
7670:
7669:
7667:
7654:
7648:
7647:
7619:
7613:
7612:
7596:
7590:
7589:
7561:
7545:
7539:
7538:
7528:
7496:
7490:
7489:
7488:
7487:
7446:
7440:
7439:
7438:
7437:
7414:
7408:
7407:
7365:
7341:
7335:
7334:
7315:10.1038/251599a0
7286:
7280:
7279:
7251:
7245:
7244:
7241:10.1121/1.381721
7216:
7207:
7206:
7195:10.1038/258317a0
7170:
7164:
7163:
7143:
7134:
7127:
7121:
7120:
7070:
7064:
7063:
7030:(6): 4143–4149.
7015:
7009:
7008:
7000:
6994:
6993:
6973:
6962:
6961:
6959:
6958:
6944:
6938:
6937:
6909:
6903:
6902:
6869:
6863:
6862:
6844:
6835:
6834:
6816:
6789:
6788:
6786:
6785:
6779:
6768:
6759:
6753:
6752:
6735:Think Complexity
6729:
6723:
6722:
6682:
6676:
6675:
6657:
6648:
6647:
6645:
6643:
6627:
6621:
6620:
6602:
6576:
6567:
6457:audio amplifiers
6409:Butterfly effect
6213:Climate dynamics
6150:
6148:
6147:
6144:{\displaystyle }
6142:
6137:
6129:
6128:
6116:
6108:
6107:
6082:
6080:
6079:
6074:
6068:
6060:
6046:
6044:
6033:
5990:James E. Cutting
5962:action potential
5960:have shown that
5912:
5910:
5909:
5904:
5902:
5897:
5888:
5886:
5885:
5880:
5878:
5877:
5853:
5852:
5836:
5834:
5833:
5828:
5816:
5814:
5813:
5808:
5797:
5796:
5780:
5778:
5777:
5772:
5770:
5769:
5764:
5763:
5755:
5744:
5742:
5741:
5736:
5734:
5733:
5706:
5705:
5696:
5695:
5668:
5667:
5651:
5649:
5648:
5643:
5631:
5629:
5628:
5623:
5621:
5620:
5611:
5588:
5587:
5582:
5581:
5573:
5556:
5554:
5553:
5548:
5546:
5545:
5536:
5517:
5515:
5514:
5509:
5504:
5480:
5478:
5477:
5472:
5467:
5442:
5440:
5439:
5434:
5414:
5413:
5408:
5407:
5399:
5361:
5356:
5326:
5325:
5320:
5319:
5311:
5276:
5271:
5241:
5240:
5235:
5234:
5226:
5209:
5204:
5183:
5182:
5164:
5162:
5161:
5156:
5154:
5153:
5126:
5125:
5109:
5107:
5106:
5101:
5099:
5098:
5071:
5070:
5065:
5064:
5056:
5039:
5037:
5036:
5031:
5001:
4999:
4998:
4993:
4981:
4979:
4978:
4973:
4962:
4961:
4935:
4933:
4932:
4927:
4922:
4921:
4916:
4915:
4907:
4887:
4885:
4884:
4879:
4871:
4870:
4852:
4851:
4846:
4845:
4837:
4824:
4816:
4813:
4805:
4796:
4794:
4783:
4778:
4777:
4768:
4767:
4749:
4748:
4736:
4728:
4725:
4720:
4705:
4697:
4688:
4686:
4685:
4680:
4678:
4673:
4672:
4671:
4650:
4649:
4644:
4643:
4635:
4621:
4619:
4611:
4606:
4601:
4600:
4599:
4590:
4589:
4571:
4570:
4557:
4555:
4547:
4533:
4532:
4513:
4511:
4510:
4505:
4482:
4481:
4454:
4453:
4440:
4438:
4437:
4432:
4427:
4416:
4380:
4378:
4377:
4372:
4351:
4349:
4348:
4343:
4328:
4326:
4325:
4320:
4315:
4296:
4294:
4293:
4288:
4286:
4281:
4271:
4270:
4234:
4233:
4208:
4184:
4182:
4181:
4176:
4159:
4158:
4153:
4152:
4144:
4113:
4112:
4107:
4106:
4098:
4073:
4072:
4071:
4058:
4057:
4039:
4038:
4015:
4013:
4012:
4007:
4005:
4004:
3980:
3977:
3959:
3957:
3956:
3951:
3939:
3937:
3936:
3931:
3929:
3928:
3919:
3918:
3900:
3899:
3887:
3879:
3876:
3871:
3856:
3848:
3843:
3838:
3837:
3836:
3827:
3826:
3808:
3807:
3794:
3792:
3784:
3770:
3769:
3746:
3744:
3743:
3738:
3736:
3735:
3719:
3717:
3716:
3711:
3709:
3704:
3657:
3637:
3636:
3628:
3624:
3604:
3592:
3584:
3579:
3578:
3562:
3560:
3559:
3556:{\displaystyle }
3554:
3508:
3506:
3505:
3500:
3492:
3491:
3486:
3485:
3477:
3466:
3464:
3463:
3458:
3446:
3444:
3443:
3438:
3427:
3426:
3421:
3420:
3412:
3405:
3404:
3399:
3398:
3390:
3374:
3373:
3365:
3355:
3353:
3352:
3347:
3345:
3344:
3339:
3338:
3330:
3319:
3317:
3316:
3311:
3309:
3308:
3303:
3302:
3294:
3283:
3281:
3280:
3275:
3264:
3263:
3255:
3245:
3243:
3242:
3237:
3216:
3214:
3213:
3208:
3196:
3194:
3193:
3188:
3034:
3032:
3031:
3026:
3024:
3023:
3007:
3005:
3004:
2999:
2994:
2992:
2991:
2983:
2980:
2970:
2969:
2964:
2960:
2955:
2941:
2936:
2935:
2925:
2922:
2912:
2876:
2874:
2873:
2868:
2857:
2856:
2853:
2843:
2841:
2840:
2835:
2830:
2828:
2827:
2825:
2824:
2823:
2820:
2813:
2812:
2811:
2808:
2801:
2792:
2788:
2783:
2779:
2778:
2777:
2774:
2760:
2755:
2754:
2751:
2742:
2737:
2733:
2732:
2731:
2728:
2714:
2709:
2708:
2705:
2701:
2677:
2675:
2674:
2669:
2667:
2666:
2665:
2662:
2648:
2646:
2645:
2640:
2638:
2637:
2636:
2633:
2619:
2617:
2616:
2611:
2606:
2604:
2603:
2595:
2592:
2582:
2581:
2576:
2575:
2570:
2556:
2547:
2544:
2534:
2510:
2508:
2507:
2502:
2490:
2488:
2487:
2482:
2454:
2452:
2451:
2446:
2438:
2423:
2421:
2420:
2415:
2403:
2401:
2400:
2395:
2393:
2381:
2379:
2378:
2373:
2361:
2359:
2358:
2353:
2331:
2329:
2328:
2323:
2321:
2320:
2290:
2274:
2272:
2271:
2266:
2264:
2263:
2251:
2235:
2233:
2232:
2227:
2225:
2224:
2220:
2204:
2188:
2186:
2185:
2180:
2168:
2166:
2165:
2160:
2145:
2143:
2142:
2137:
2132:
2116:
2114:
2113:
2108:
2106:
2105:
2096:
2080:
2078:
2077:
2072:
2070:
2069:
2065:
2052:
2036:
2034:
2033:
2028:
2013:
2011:
2010:
2005:
2000:
1984:
1982:
1981:
1976:
1974:
1973:
1964:
1948:
1946:
1945:
1940:
1938:
1937:
1933:
1920:
1899:
1897:
1896:
1891:
1886:
1870:
1868:
1867:
1862:
1860:
1859:
1850:
1834:
1832:
1831:
1826:
1821:
1800:
1798:
1797:
1792:
1787:
1771:
1769:
1768:
1763:
1758:
1742:
1740:
1739:
1734:
1732:
1727:
1725:
1704:
1702:
1701:
1696:
1673:
1671:
1670:
1665:
1654:
1653:
1635:
1633:
1632:
1627:
1616:
1615:
1594:
1590:
1587:
1585:
1584:
1579:
1557:
1555:
1554:
1549:
1537:
1535:
1534:
1529:
1517:
1515:
1514:
1509:
1507:
1506:
1490:
1488:
1487:
1482:
1480:
1479:
1460:
1458:
1457:
1452:
1450:
1448:
1447:
1435:
1426:
1424:
1423:
1418:
1406:
1404:
1403:
1398:
1396:
1394:
1393:
1381:
1372:
1370:
1369:
1364:
1362:
1354:
1313:
1311:
1310:
1305:
1300:
1296:
1295:
1279:
1274:
1263:
1254:
1248:
1244:
1241:
1231:
1222:
1177:
1171:
1163:
1159:
1146:
1138:
1112:
1110:
1109:
1104:
972:) to describe 1/
966:fractional noise
933:condensed-matter
924:
922:
921:
916:
887:
886:
855:
854:
838:
834:
833:
832:
796:
791:
783:
770:
767:
766:
754:
753:
744:
743:
742:
730:
727:
712:
706:
705:
697:
667:
665:
664:
659:
644:
642:
641:
636:
634:
633:
610:
608:
607:
602:
600:
599:
582:
580:
579:
574:
545:
544:
516:
515:
499:
498:
486:
481:
467:
456:
451:
450:
441:
438:
429:
420:
419:
390:
388:
387:
382:
370:
368:
367:
362:
346:
344:
343:
338:
317:
315:
314:
309:
304:
302:
301:
289:
234:
233:
214:
149:fractional noise
144:
143:
139:
80:
73:
66:
19:
18:
10301:
10300:
10296:
10295:
10294:
10292:
10291:
10290:
10266:
10265:
10264:
10255:
10229:Non-local means
10202:
10183:Low-pass filter
10168:
10162:
10148:Noise generator
10138:Colors of noise
10116:
10023:
10019:
10008:
10004:
9953:
9875:
9869:
9849:Coherent noise
9825:(thermal noise)
9755:
9679:
9665:Noise reduction
9623:
9617:
9557:
9539:
9459:(10): 157–176.
9421:(23): 541–567.
9396:
9373:
9362:
9318:Physical Review
9242:10.1.1.136.1345
9214:
9120:
9115:
9114:
9095:
9092:
9091:
9089:
9085:
9080:
9070:
9068:
9058:
9054:
9041:
9037:
9027:
9025:
9019:Yamaha Insights
9011:
9007:
8997:
8995:
8985:
8981:
8974:
8960:
8956:
8907:
8903:
8848:
8844:
8821:
8817:
8809:
8798:
8792:
8788:
8779:
8777:
8769:
8768:
8764:
8755:
8753:
8745:
8744:
8740:
8701:
8697:
8689:physics/0204033
8680:
8676:
8645:
8641:
8592:
8588:
8549:
8545:
8530:
8526:
8486:
8476:
8469:
8414:
8410:
8355:
8351:
8336:
8322:
8318:
8257:
8253:
8243:
8241:
8231:
8227:
8217:
8215:
8209:
8205:
8150:
8146:
8085:
8081:
8046:
8042:
8038:, Prentice–Hall
8033:
8029:
7986:
7982:
7949:
7945:
7908:
7904:
7867:
7863:
7831:10.1.1.136.1992
7808:
7804:
7773:
7769:
7718:
7714:
7709:Wayback Machine
7691:
7687:
7678:
7677:
7673:
7665:
7661:
7655:
7651:
7620:
7616:
7597:
7593:
7578:
7546:
7542:
7497:
7493:
7485:
7483:
7473:
7447:
7443:
7435:
7433:
7415:
7411:
7342:
7338:
7287:
7283:
7252:
7248:
7217:
7210:
7171:
7167:
7144:
7137:
7128:
7124:
7071:
7067:
7016:
7012:
7001:
6997:
6974:
6965:
6956:
6954:
6946:
6945:
6941:
6910:
6906:
6899:10.1137/1010093
6870:
6866:
6859:
6845:
6838:
6817:
6792:
6783:
6781:
6777:
6766:
6760:
6756:
6746:
6730:
6726:
6683:
6679:
6672:
6658:
6651:
6641:
6639:
6629:
6628:
6624:
6600:10.1.1.136.1345
6574:
6568:
6561:
6557:
6552:
6498:Colors of noise
6473:
6445:audio equalizer
6421:
6304:
6298:
6235:Brownian motion
6227:
6215:
6167:
6130:
6124:
6120:
6109:
6100:
6096:
6091:
6088:
6087:
6059:
6037:
6032:
6029:
6026:
6025:
6016:
6010:
5922:
5896:
5894:
5891:
5890:
5870:
5866:
5848:
5844:
5842:
5839:
5838:
5822:
5819:
5818:
5792:
5788:
5786:
5783:
5782:
5765:
5754:
5753:
5752:
5750:
5747:
5746:
5723:
5719:
5701:
5697:
5685:
5681:
5663:
5659:
5657:
5654:
5653:
5637:
5634:
5633:
5616:
5612:
5607:
5583:
5572:
5571:
5570:
5562:
5559:
5558:
5541:
5537:
5532:
5527:
5524:
5523:
5521:
5500:
5486:
5483:
5482:
5481:with bandwidth
5463:
5452:
5449:
5448:
5409:
5398:
5397:
5396:
5357:
5352:
5321:
5310:
5309:
5308:
5272:
5267:
5236:
5225:
5224:
5223:
5205:
5200:
5178:
5174:
5172:
5169:
5168:
5143:
5139:
5121:
5117:
5115:
5112:
5111:
5091:
5087:
5066:
5055:
5054:
5053:
5045:
5042:
5041:
5007:
5004:
5003:
4987:
4984:
4983:
4957:
4953:
4951:
4948:
4947:
4917:
4906:
4905:
4904:
4893:
4890:
4889:
4866:
4862:
4847:
4836:
4835:
4834:
4815:
4806:
4801:
4787:
4782:
4773:
4769:
4757:
4753:
4744:
4740:
4727:
4721:
4710:
4696:
4694:
4691:
4690:
4667:
4663:
4645:
4634:
4633:
4632:
4622:
4620:
4610:
4595:
4591:
4579:
4575:
4566:
4562:
4558:
4556:
4546:
4528:
4524:
4522:
4519:
4518:
4477:
4476:
4449:
4448:
4446:
4443:
4442:
4423:
4412:
4386:
4383:
4382:
4357:
4354:
4353:
4334:
4331:
4330:
4329:and wavelength
4311:
4306:
4303:
4302:
4251:
4247:
4217:
4213:
4209:
4207:
4190:
4187:
4186:
4154:
4143:
4142:
4141:
4108:
4097:
4096:
4095:
4067:
4066:
4062:
4047:
4043:
4034:
4030:
4028:
4025:
4024:
3997:
3993:
3976:
3965:
3962:
3961:
3945:
3942:
3941:
3924:
3920:
3908:
3904:
3895:
3891:
3878:
3872:
3861:
3847:
3832:
3828:
3816:
3812:
3803:
3799:
3795:
3793:
3783:
3765:
3761:
3759:
3756:
3755:
3731:
3727:
3725:
3722:
3721:
3658:
3656:
3627:
3626:
3605:
3597:
3583:
3574:
3570:
3568:
3565:
3564:
3518:
3515:
3514:
3487:
3476:
3475:
3474:
3472:
3469:
3468:
3452:
3449:
3448:
3422:
3411:
3410:
3409:
3400:
3389:
3388:
3387:
3364:
3363:
3361:
3358:
3357:
3340:
3329:
3328:
3327:
3325:
3322:
3321:
3304:
3293:
3292:
3291:
3289:
3286:
3285:
3254:
3253:
3251:
3248:
3247:
3222:
3219:
3218:
3202:
3199:
3198:
3173:
3170:
3169:
3127:
3121:
3045:
3019:
3015:
3013:
3010:
3009:
2982:
2976:
2971:
2942:
2940:
2931:
2927:
2926:
2924:
2918:
2913:
2911:
2894:
2891:
2890:
2887:
2852:
2851:
2849:
2846:
2845:
2819:
2818:
2814:
2807:
2806:
2802:
2800:
2793:
2773:
2772:
2768:
2761:
2759:
2750:
2749:
2727:
2726:
2722:
2715:
2713:
2704:
2703:
2702:
2700:
2683:
2680:
2679:
2661:
2660:
2656:
2654:
2651:
2650:
2632:
2631:
2627:
2625:
2622:
2621:
2594:
2588:
2583:
2557:
2555:
2548:
2546:
2540:
2535:
2533:
2516:
2513:
2512:
2496:
2493:
2492:
2476:
2473:
2472:
2469:
2461:
2459:Autocorrelation
2434:
2429:
2426:
2425:
2409:
2406:
2405:
2389:
2387:
2384:
2383:
2367:
2364:
2363:
2347:
2344:
2343:
2340:
2295:
2291:
2286:
2281:
2278:
2277:
2256:
2252:
2247:
2242:
2239:
2238:
2216:
2209:
2205:
2200:
2195:
2192:
2191:
2174:
2171:
2170:
2154:
2151:
2150:
2128:
2123:
2120:
2119:
2101:
2097:
2092:
2087:
2084:
2083:
2061:
2057:
2053:
2048:
2043:
2040:
2039:
2022:
2019:
2018:
1996:
1991:
1988:
1987:
1969:
1965:
1960:
1955:
1952:
1951:
1929:
1925:
1921:
1916:
1911:
1908:
1907:
1882:
1877:
1874:
1873:
1855:
1851:
1846:
1841:
1838:
1837:
1817:
1812:
1809:
1808:
1783:
1778:
1775:
1774:
1754:
1749:
1746:
1745:
1726:
1721:
1716:
1713:
1712:
1681:
1678:
1677:
1649:
1645:
1643:
1640:
1639:
1611:
1607:
1605:
1602:
1601:
1567:
1564:
1563:
1543:
1540:
1539:
1523:
1520:
1519:
1502:
1498:
1496:
1493:
1492:
1475:
1471:
1469:
1466:
1465:
1443:
1439:
1434:
1432:
1429:
1428:
1412:
1409:
1408:
1389:
1385:
1380:
1378:
1375:
1374:
1353:
1351:
1348:
1347:
1344:
1330:
1324:of dimensions.
1264:
1262:
1261:
1243:
1227:
1223:
1212:
1167:
1158:
1151:
1147:
1137:
1120:
1117:
1116:
1098:
1095:
1094:
1082:
994:
941:non-equilibrium
879:
875:
847:
843:
825:
821:
784:
782:
781:
777:
762:
758:
749:
745:
735:
731:
729:
717:
698:
696:
673:
670:
669:
653:
650:
649:
629:
625:
623:
620:
619:
595:
591:
589:
586:
585:
540:
536:
511:
507:
494:
490:
468:
466:
446:
442:
440:
434:
418:
398:
395:
394:
376:
373:
372:
356:
353:
352:
332:
329:
328:
297:
293:
288:
271:
268:
267:
262:
261:
253:
251:
250:
249:
248:
235:
228:
225:
218:
212:
207:
141:
137:
136:
109:
102:
95:
84:
23:Colors of noise
17:
12:
11:
5:
10299:
10289:
10288:
10283:
10278:
10261:
10260:
10257:
10256:
10254:
10253:
10248:
10242:
10237:
10231:
10226:
10221:
10216:
10210:
10208:
10204:
10203:
10201:
10200:
10195:
10190:
10185:
10179:
10177:
10170:
10164:
10163:
10161:
10160:
10155:
10150:
10145:
10140:
10135:
10130:
10124:
10122:
10121:Related topics
10118:
10117:
10115:
10114:
10104:
10094:
10084:
10079:
10061:
10047:
10037:
10027:
10021:
10017:
10012:
10006:
10002:
9997:
9990:
9976:
9961:
9959:
9955:
9954:
9952:
9951:
9946:
9941:
9936:
9930:
9925:
9920:
9915:
9910:
9905:
9900:
9895:
9890:
9885:
9879:
9877:
9871:
9870:
9868:
9867:
9866:
9865:
9860:
9858:Gradient noise
9855:
9847:
9842:
9837:
9831:
9826:
9820:
9815:
9810:
9805:
9803:Gaussian noise
9800:
9795:
9790:
9785:
9783:Brownian noise
9780:
9775:
9770:
9763:
9761:
9760:Class of noise
9757:
9756:
9754:
9753:
9748:
9746:Transportation
9743:
9738:
9733:
9728:
9723:
9718:
9713:
9708:
9703:
9698:
9693:
9687:
9685:
9681:
9680:
9678:
9677:
9672:
9667:
9662:
9657:
9652:
9647:
9642:
9637:
9631:
9629:
9625:
9624:
9616:
9615:
9608:
9601:
9593:
9587:
9586:
9581:
9576:
9563:
9556:
9555:External links
9553:
9552:
9551:
9537:
9512:
9494:(3): 212–218.
9477:
9439:
9401:
9384:(4): 103–119.
9366:
9360:
9343:
9312:
9283:10.1.1.24.4883
9276:(2): 161–209.
9263:
9207:
9189:(3): 497–516.
9172:
9138:(4): 381–384.
9119:
9116:
9113:
9112:
9099:
9082:
9081:
9079:
9078:
9052:
9035:
9005:
8979:
8972:
8954:
8917:(8): 1650086.
8901:
8842:
8815:
8812:on 2011-10-04.
8786:
8762:
8738:
8695:
8674:
8639:
8586:
8543:
8524:
8467:
8408:
8349:
8334:
8316:
8271:(10): 108701.
8251:
8225:
8203:
8144:
8099:(8): 549–555.
8079:
8060:(4): 585–599.
8040:
8027:
7980:
7943:
7924:(3): 497–516.
7902:
7883:(2): 537–571.
7861:
7802:
7783:(4): 296–301.
7767:
7712:
7702:original study
7685:
7671:
7649:
7630:(3): 331–350.
7614:
7591:
7576:
7540:
7491:
7471:
7441:
7409:
7336:
7281:
7246:
7227:(1): 258–263.
7208:
7165:
7135:
7122:
7087:(4): 381–384.
7065:
7010:
6995:
6984:(4): 103–119.
6963:
6939:
6920:(1): 260–267.
6904:
6885:(4): 422–437.
6864:
6857:
6836:
6790:
6771:Wireless World
6754:
6744:
6724:
6697:(3): 227–231.
6677:
6670:
6649:
6636:Sound on Sound
6622:
6558:
6556:
6553:
6551:
6550:
6545:
6540:
6535:
6530:
6525:
6520:
6515:
6510:
6505:
6500:
6495:
6490:
6488:Brownian noise
6485:
6480:
6474:
6472:
6469:
6420:
6417:
6308:semiconductors
6297:
6294:
6271:Hurst exponent
6259:Brownian noise
6226:
6223:
6219:climate system
6214:
6211:
6166:
6163:
6140:
6136:
6133:
6127:
6123:
6119:
6115:
6112:
6106:
6103:
6099:
6095:
6071:
6066:
6063:
6058:
6055:
6052:
6049:
6043:
6040:
6036:
6012:Main article:
6009:
6006:
5921:
5918:
5900:
5876:
5873:
5869:
5865:
5862:
5859:
5856:
5851:
5847:
5826:
5806:
5803:
5800:
5795:
5791:
5768:
5761:
5758:
5732:
5729:
5726:
5722:
5718:
5715:
5712:
5709:
5704:
5700:
5694:
5691:
5688:
5684:
5680:
5677:
5674:
5671:
5666:
5662:
5641:
5619:
5615:
5610:
5606:
5603:
5600:
5597:
5594:
5591:
5586:
5579:
5576:
5569:
5566:
5544:
5540:
5535:
5531:
5507:
5503:
5499:
5496:
5493:
5490:
5470:
5466:
5462:
5459:
5456:
5432:
5429:
5426:
5423:
5420:
5417:
5412:
5405:
5402:
5395:
5392:
5389:
5386:
5383:
5380:
5377:
5374:
5371:
5368:
5365:
5360:
5355:
5351:
5347:
5344:
5341:
5338:
5335:
5332:
5329:
5324:
5317:
5314:
5307:
5304:
5301:
5298:
5295:
5292:
5289:
5286:
5283:
5280:
5275:
5270:
5266:
5262:
5259:
5256:
5253:
5250:
5247:
5244:
5239:
5232:
5229:
5222:
5219:
5216:
5213:
5208:
5203:
5199:
5195:
5192:
5189:
5186:
5181:
5177:
5152:
5149:
5146:
5142:
5138:
5135:
5132:
5129:
5124:
5120:
5097:
5094:
5090:
5086:
5083:
5080:
5077:
5074:
5069:
5062:
5059:
5052:
5049:
5029:
5026:
5023:
5020:
5017:
5014:
5011:
4991:
4971:
4968:
4965:
4960:
4956:
4938:power spectrum
4925:
4920:
4913:
4910:
4903:
4900:
4897:
4877:
4874:
4869:
4865:
4861:
4858:
4855:
4850:
4843:
4840:
4833:
4830:
4827:
4822:
4819:
4812:
4809:
4804:
4800:
4793:
4790:
4786:
4781:
4776:
4772:
4766:
4763:
4760:
4756:
4752:
4747:
4743:
4739:
4734:
4731:
4724:
4719:
4716:
4713:
4709:
4703:
4700:
4676:
4670:
4666:
4662:
4659:
4656:
4653:
4648:
4641:
4638:
4631:
4628:
4625:
4617:
4614:
4609:
4604:
4598:
4594:
4588:
4585:
4582:
4578:
4574:
4569:
4565:
4561:
4553:
4550:
4545:
4542:
4539:
4536:
4531:
4527:
4503:
4500:
4497:
4494:
4491:
4488:
4485:
4480:
4475:
4472:
4469:
4466:
4463:
4460:
4457:
4452:
4430:
4426:
4422:
4419:
4415:
4411:
4408:
4405:
4402:
4399:
4396:
4393:
4390:
4370:
4367:
4364:
4361:
4341:
4338:
4318:
4314:
4310:
4284:
4280:
4277:
4274:
4269:
4266:
4263:
4260:
4257:
4254:
4250:
4246:
4243:
4240:
4237:
4232:
4229:
4226:
4223:
4220:
4216:
4212:
4206:
4203:
4200:
4197:
4194:
4174:
4171:
4168:
4165:
4162:
4157:
4150:
4147:
4140:
4137:
4134:
4131:
4128:
4125:
4122:
4119:
4116:
4111:
4104:
4101:
4094:
4091:
4088:
4085:
4082:
4079:
4076:
4070:
4065:
4061:
4056:
4053:
4050:
4046:
4042:
4037:
4033:
4003:
4000:
3996:
3992:
3989:
3986:
3983:
3975:
3972:
3969:
3949:
3927:
3923:
3917:
3914:
3911:
3907:
3903:
3898:
3894:
3890:
3885:
3882:
3875:
3870:
3867:
3864:
3860:
3854:
3851:
3846:
3841:
3835:
3831:
3825:
3822:
3819:
3815:
3811:
3806:
3802:
3798:
3790:
3787:
3782:
3779:
3776:
3773:
3768:
3764:
3752:Allan variance
3734:
3730:
3707:
3703:
3700:
3697:
3694:
3691:
3688:
3685:
3682:
3679:
3676:
3673:
3670:
3667:
3664:
3661:
3655:
3652:
3649:
3646:
3643:
3640:
3634:
3631:
3623:
3620:
3617:
3614:
3611:
3608:
3603:
3600:
3596:
3590:
3587:
3582:
3577:
3573:
3552:
3549:
3546:
3543:
3540:
3537:
3534:
3531:
3528:
3525:
3522:
3498:
3495:
3490:
3483:
3480:
3467:, we can have
3456:
3436:
3433:
3430:
3425:
3418:
3415:
3408:
3403:
3396:
3393:
3386:
3383:
3380:
3377:
3371:
3368:
3343:
3336:
3333:
3307:
3300:
3297:
3273:
3270:
3267:
3261:
3258:
3235:
3232:
3229:
3226:
3206:
3186:
3183:
3180:
3177:
3125:Allan variance
3123:Main article:
3120:
3117:
3110:(1978) in his
3108:Martin Gardner
3089:meteorological
3044:
3041:
3022:
3018:
2997:
2989:
2986:
2979:
2975:
2967:
2963:
2958:
2954:
2951:
2948:
2945:
2939:
2934:
2930:
2921:
2917:
2910:
2907:
2904:
2901:
2898:
2886:
2883:
2866:
2863:
2860:
2833:
2817:
2805:
2799:
2796:
2791:
2786:
2782:
2771:
2767:
2764:
2758:
2748:
2745:
2740:
2736:
2725:
2721:
2718:
2712:
2699:
2696:
2693:
2690:
2687:
2659:
2630:
2609:
2601:
2598:
2591:
2587:
2579:
2573:
2569:
2566:
2563:
2560:
2554:
2551:
2543:
2539:
2532:
2529:
2526:
2523:
2520:
2500:
2480:
2468:
2465:
2460:
2457:
2444:
2441:
2437:
2433:
2413:
2392:
2371:
2351:
2339:
2336:
2333:
2332:
2319:
2316:
2313:
2310:
2307:
2304:
2301:
2298:
2294:
2289:
2285:
2275:
2262:
2259:
2255:
2250:
2246:
2236:
2223:
2219:
2215:
2212:
2208:
2203:
2199:
2189:
2178:
2158:
2147:
2146:
2135:
2131:
2127:
2117:
2104:
2100:
2095:
2091:
2081:
2068:
2064:
2060:
2056:
2051:
2047:
2037:
2026:
2015:
2014:
2003:
1999:
1995:
1985:
1972:
1968:
1963:
1959:
1949:
1936:
1932:
1928:
1924:
1919:
1915:
1905:
1901:
1900:
1889:
1885:
1881:
1871:
1858:
1854:
1849:
1845:
1835:
1824:
1820:
1816:
1806:
1802:
1801:
1790:
1786:
1782:
1772:
1761:
1757:
1753:
1743:
1730:
1724:
1720:
1710:
1706:
1705:
1694:
1691:
1688:
1685:
1674:
1663:
1660:
1657:
1652:
1648:
1636:
1625:
1622:
1619:
1614:
1610:
1598:
1577:
1574:
1571:
1547:
1527:
1505:
1501:
1478:
1474:
1446:
1442:
1438:
1416:
1392:
1388:
1384:
1360:
1357:
1343:
1340:
1329:
1326:
1303:
1299:
1294:
1291:
1288:
1285:
1282:
1277:
1273:
1270:
1267:
1260:
1257:
1251:
1247:
1240:
1237:
1234:
1230:
1226:
1221:
1218:
1215:
1211:
1207:
1204:
1201:
1198:
1195:
1192:
1189:
1186:
1183:
1180:
1174:
1170:
1166:
1162:
1157:
1154:
1150:
1144:
1141:
1136:
1133:
1130:
1127:
1124:
1102:
1081:
1078:
1012:(right) on an
993:
990:
914:
911:
908:
905:
902:
899:
896:
893:
890:
885:
882:
878:
873:
870:
867:
864:
861:
858:
853:
850:
846:
841:
837:
831:
828:
824:
820:
817:
814:
811:
808:
805:
802:
799:
794:
790:
787:
780:
776:
773:
765:
761:
757:
752:
748:
741:
738:
734:
726:
723:
720:
716:
709:
704:
701:
695:
692:
689:
686:
683:
680:
677:
657:
632:
628:
598:
594:
572:
569:
566:
563:
560:
557:
554:
551:
548:
543:
539:
534:
531:
528:
525:
522:
519:
514:
510:
505:
502:
497:
493:
489:
484:
480:
477:
474:
471:
465:
462:
459:
454:
449:
445:
437:
433:
426:
423:
417:
414:
411:
408:
405:
402:
380:
360:
336:
307:
300:
296:
292:
287:
284:
281:
278:
275:
252:
246:peak amplitude
236:
226:
221:
220:
219:
210:
209:
208:
206:
203:
163:such that the
86:
85:
83:
82:
75:
68:
60:
57:
56:
55:
54:
49:
44:
42:Red (Brownian)
39:
34:
26:
25:
15:
9:
6:
4:
3:
2:
10298:
10287:
10284:
10282:
10279:
10277:
10274:
10273:
10271:
10252:
10249:
10246:
10243:
10241:
10238:
10235:
10232:
10230:
10227:
10225:
10222:
10220:
10217:
10215:
10214:Gaussian blur
10212:
10211:
10209:
10205:
10199:
10196:
10194:
10191:
10189:
10188:Median filter
10186:
10184:
10181:
10180:
10178:
10174:
10171:
10165:
10159:
10156:
10154:
10151:
10149:
10146:
10144:
10141:
10139:
10136:
10134:
10131:
10129:
10126:
10125:
10123:
10119:
10112:
10108:
10105:
10102:
10098:
10095:
10092:
10088:
10085:
10083:
10080:
10077:
10073:
10069:
10065:
10062:
10059:
10055:
10051:
10048:
10045:
10041:
10038:
10035:
10031:
10028:
10025:
10024:
10013:
10010:
10009:
9998:
9996:
9995:
9991:
9988:
9984:
9980:
9977:
9974:
9970:
9966:
9963:
9962:
9960:
9956:
9950:
9947:
9945:
9942:
9940:
9937:
9934:
9931:
9929:
9926:
9924:
9923:Noise shaping
9921:
9919:
9916:
9914:
9911:
9909:
9906:
9904:
9901:
9899:
9896:
9894:
9891:
9889:
9886:
9884:
9881:
9880:
9878:
9872:
9864:
9861:
9859:
9856:
9854:
9851:
9850:
9848:
9846:
9843:
9841:
9838:
9836:(or q. noise)
9835:
9832:
9830:
9827:
9824:
9821:
9819:
9816:
9814:
9811:
9809:
9806:
9804:
9801:
9799:
9798:Flicker noise
9796:
9794:
9791:
9789:
9786:
9784:
9781:
9779:
9776:
9774:
9771:
9768:
9765:
9764:
9762:
9758:
9752:
9749:
9747:
9744:
9742:
9741:Sound masking
9739:
9737:
9734:
9732:
9729:
9727:
9724:
9722:
9719:
9717:
9714:
9712:
9709:
9707:
9704:
9702:
9699:
9697:
9694:
9692:
9689:
9688:
9686:
9682:
9676:
9673:
9671:
9668:
9666:
9663:
9661:
9658:
9656:
9653:
9651:
9650:Noise control
9648:
9646:
9643:
9641:
9638:
9636:
9633:
9632:
9630:
9626:
9621:
9614:
9609:
9607:
9602:
9600:
9595:
9594:
9591:
9585:
9582:
9580:
9577:
9575:
9573:
9569:
9564:
9562:
9559:
9558:
9548:
9544:
9540:
9534:
9530:
9526:
9522:
9518:
9513:
9509:
9505:
9501:
9497:
9493:
9489:
9488:
9483:
9478:
9474:
9470:
9466:
9462:
9458:
9454:
9453:
9448:
9444:
9440:
9436:
9432:
9428:
9424:
9420:
9416:
9415:
9410:
9406:
9402:
9395:
9391:
9387:
9383:
9379:
9372:
9367:
9363:
9357:
9353:
9349:
9344:
9340:
9336:
9332:
9328:
9324:
9320:
9319:
9313:
9309:
9305:
9301:
9297:
9293:
9289:
9284:
9279:
9275:
9271:
9270:
9264:
9260:
9256:
9252:
9248:
9243:
9238:
9234:
9230:
9226:
9222:
9221:
9213:
9208:
9204:
9200:
9196:
9192:
9188:
9184:
9183:
9178:
9173:
9169:
9165:
9161:
9157:
9153:
9149:
9145:
9141:
9137:
9133:
9132:
9127:
9122:
9121:
9097:
9087:
9083:
9067:
9063:
9056:
9048:
9047:
9039:
9024:
9020:
9016:
9009:
8994:
8990:
8983:
8975:
8973:9781351768184
8969:
8965:
8958:
8950:
8946:
8942:
8938:
8934:
8930:
8925:
8920:
8916:
8912:
8905:
8897:
8893:
8888:
8883:
8879:
8875:
8870:
8865:
8861:
8857:
8853:
8846:
8838:
8834:
8830:
8826:
8819:
8808:
8804:
8797:
8790:
8776:
8772:
8766:
8752:
8748:
8742:
8734:
8730:
8726:
8722:
8718:
8714:
8710:
8706:
8699:
8690:
8685:
8678:
8670:
8666:
8662:
8658:
8654:
8650:
8643:
8635:
8631:
8627:
8623:
8619:
8615:
8610:
8605:
8602:(1): 89–142.
8601:
8597:
8590:
8582:
8578:
8574:
8570:
8566:
8562:
8558:
8554:
8547:
8539:
8535:
8528:
8520:
8516:
8512:
8508:
8504:
8500:
8497:(6): 066120.
8496:
8492:
8485:
8483:
8474:
8472:
8463:
8459:
8454:
8449:
8445:
8441:
8436:
8431:
8428:(1): 011019.
8427:
8423:
8419:
8412:
8404:
8400:
8395:
8390:
8386:
8382:
8377:
8372:
8369:(2): 023029.
8368:
8364:
8360:
8353:
8345:
8341:
8337:
8335:9780511674983
8331:
8327:
8320:
8312:
8308:
8304:
8300:
8296:
8292:
8288:
8284:
8279:
8274:
8270:
8266:
8262:
8255:
8240:
8236:
8229:
8214:
8207:
8199:
8195:
8190:
8185:
8180:
8175:
8171:
8167:
8163:
8159:
8155:
8148:
8140:
8136:
8132:
8128:
8124:
8120:
8116:
8112:
8107:
8102:
8098:
8094:
8090:
8083:
8075:
8071:
8067:
8063:
8059:
8055:
8051:
8044:
8037:
8031:
8023:
8019:
8015:
8011:
8007:
8003:
7999:
7995:
7991:
7984:
7976:
7972:
7968:
7964:
7960:
7956:
7955:
7947:
7939:
7935:
7931:
7927:
7923:
7919:
7918:
7913:
7906:
7898:
7894:
7890:
7886:
7882:
7878:
7877:
7872:
7865:
7857:
7853:
7849:
7845:
7841:
7837:
7832:
7827:
7823:
7819:
7818:
7813:
7806:
7798:
7794:
7790:
7786:
7782:
7778:
7771:
7763:
7759:
7755:
7751:
7747:
7743:
7739:
7735:
7731:
7727:
7723:
7716:
7710:
7706:
7703:
7699:
7695:
7689:
7681:
7675:
7664:
7659:
7653:
7645:
7641:
7637:
7633:
7629:
7625:
7618:
7610:
7606:
7602:
7595:
7587:
7583:
7579:
7573:
7569:
7565:
7560:
7555:
7551:
7544:
7536:
7532:
7527:
7522:
7518:
7514:
7510:
7506:
7502:
7495:
7482:
7478:
7474:
7468:
7464:
7460:
7456:
7452:
7445:
7432:
7428:
7424:
7420:
7413:
7405:
7401:
7397:
7393:
7389:
7385:
7381:
7377:
7373:
7369:
7364:
7359:
7355:
7351:
7347:
7340:
7332:
7328:
7324:
7320:
7316:
7312:
7308:
7304:
7300:
7296:
7292:
7285:
7277:
7273:
7269:
7265:
7261:
7257:
7250:
7242:
7238:
7234:
7230:
7226:
7222:
7215:
7213:
7204:
7200:
7196:
7192:
7188:
7184:
7180:
7176:
7169:
7161:
7157:
7153:
7149:
7142:
7140:
7132:
7126:
7118:
7114:
7110:
7106:
7102:
7098:
7094:
7090:
7086:
7082:
7081:
7076:
7069:
7061:
7057:
7053:
7049:
7045:
7041:
7037:
7033:
7029:
7025:
7021:
7014:
7006:
6999:
6991:
6987:
6983:
6979:
6972:
6970:
6968:
6953:
6949:
6943:
6935:
6931:
6927:
6923:
6919:
6915:
6908:
6900:
6896:
6892:
6888:
6884:
6880:
6879:
6874:
6868:
6860:
6854:
6850:
6843:
6841:
6832:
6828:
6824:
6823:
6815:
6813:
6811:
6809:
6807:
6805:
6803:
6801:
6799:
6797:
6795:
6776:
6772:
6765:
6758:
6751:
6747:
6741:
6737:
6736:
6728:
6720:
6716:
6712:
6708:
6704:
6700:
6696:
6692:
6688:
6681:
6673:
6671:0-88188-900-8
6667:
6663:
6656:
6654:
6638:
6637:
6632:
6626:
6618:
6614:
6610:
6606:
6601:
6596:
6592:
6588:
6584:
6580:
6573:
6566:
6564:
6559:
6549:
6546:
6544:
6543:Sound masking
6541:
6539:
6536:
6534:
6531:
6529:
6526:
6524:
6521:
6519:
6516:
6514:
6513:Flicker noise
6511:
6509:
6506:
6504:
6501:
6499:
6496:
6494:
6491:
6489:
6486:
6484:
6481:
6479:
6476:
6475:
6468:
6466:
6462:
6458:
6454:
6449:
6446:
6442:
6438:
6434:
6430:
6426:
6419:Audio testing
6416:
6414:
6410:
6406:
6402:
6398:
6394:
6390:
6389:supersymmetry
6386:
6382:
6378:
6373:
6371:
6367:
6363:
6359:
6354:
6352:
6348:
6344:
6340:
6336:
6332:
6328:
6324:
6320:
6316:
6311:
6309:
6303:
6293:
6291:
6287:
6283:
6279:
6275:
6272:
6268:
6264:
6260:
6256:
6252:
6248:
6244:
6241:that equals 4
6240:
6236:
6232:
6222:
6220:
6210:
6208:
6204:
6200:
6196:
6192:
6188:
6184:
6176:
6171:
6162:
6159:
6157:
6152:
6125:
6121:
6117:
6104:
6101:
6097:
6083:
6069:
6064:
6061:
6056:
6053:
6050:
6047:
6041:
6038:
6034:
6022:
6015:
6014:Flicker noise
6005:
6003:
6002:reaction time
5997:
5995:
5991:
5987:
5983:
5979:
5975:
5974:mental states
5970:
5967:
5963:
5959:
5955:
5951:
5947:
5943:
5939:
5935:
5931:
5927:
5917:
5914:
5898:
5874:
5871:
5867:
5863:
5857:
5849:
5845:
5824:
5801:
5793:
5789:
5766:
5759:
5756:
5730:
5727:
5724:
5720:
5716:
5710:
5702:
5698:
5692:
5689:
5686:
5682:
5678:
5672:
5664:
5660:
5639:
5617:
5613:
5608:
5604:
5601:
5595:
5584:
5577:
5574:
5564:
5542:
5538:
5533:
5529:
5519:
5505:
5501:
5497:
5494:
5491:
5468:
5464:
5460:
5457:
5454:
5446:
5430:
5427:
5421:
5410:
5403:
5400:
5390:
5387:
5381:
5378:
5369:
5363:
5353:
5349:
5345:
5342:
5339:
5333:
5322:
5315:
5312:
5302:
5299:
5293:
5284:
5278:
5268:
5264:
5260:
5257:
5254:
5248:
5237:
5230:
5227:
5220:
5217:
5211:
5201:
5197:
5193:
5187:
5179:
5175:
5150:
5147:
5144:
5140:
5136:
5130:
5122:
5118:
5095:
5092:
5088:
5084:
5078:
5067:
5060:
5057:
5047:
5024:
5015:
5009:
4989:
4966:
4958:
4954:
4945:
4941:
4939:
4918:
4911:
4908:
4901:
4898:
4875:
4872:
4867:
4859:
4848:
4841:
4838:
4831:
4828:
4820:
4817:
4810:
4807:
4802:
4798:
4791:
4788:
4784:
4779:
4774:
4764:
4761:
4758:
4754:
4750:
4745:
4741:
4732:
4729:
4722:
4717:
4714:
4711:
4707:
4701:
4698:
4668:
4660:
4657:
4646:
4639:
4636:
4629:
4626:
4615:
4612:
4607:
4596:
4586:
4583:
4580:
4576:
4572:
4567:
4563:
4551:
4548:
4543:
4537:
4529:
4525:
4515:
4498:
4495:
4486:
4473:
4467:
4458:
4428:
4424:
4417:
4413:
4409:
4403:
4400:
4394:
4388:
4365:
4359:
4339:
4336:
4316:
4312:
4308:
4300:
4282:
4275:
4264:
4261:
4258:
4255:
4248:
4244:
4238:
4227:
4224:
4221:
4214:
4210:
4204:
4198:
4192:
4169:
4166:
4155:
4148:
4145:
4138:
4135:
4129:
4126:
4123:
4117:
4109:
4102:
4099:
4089:
4086:
4083:
4080:
4074:
4063:
4059:
4054:
4051:
4048:
4044:
4040:
4035:
4031:
4021:
4019:
4001:
3998:
3994:
3990:
3987:
3984:
3978: seconds
3973:
3967:
3947:
3925:
3915:
3912:
3909:
3905:
3901:
3896:
3892:
3883:
3880:
3873:
3868:
3865:
3862:
3858:
3852:
3849:
3844:
3833:
3823:
3820:
3817:
3813:
3809:
3804:
3800:
3788:
3785:
3780:
3774:
3766:
3762:
3753:
3748:
3732:
3728:
3705:
3698:
3695:
3689:
3686:
3680:
3674:
3671:
3668:
3659:
3653:
3650:
3647:
3641:
3632:
3629:
3621:
3615:
3612:
3609:
3601:
3598:
3594:
3588:
3585:
3580:
3575:
3571:
3547:
3541:
3538:
3535:
3529:
3526:
3523:
3510:
3496:
3493:
3488:
3481:
3478:
3454:
3431:
3423:
3416:
3413:
3406:
3401:
3394:
3391:
3384:
3378:
3369:
3366:
3341:
3334:
3331:
3305:
3298:
3295:
3268:
3259:
3256:
3230:
3224:
3204:
3181:
3175:
3167:
3163:
3162:atomic clocks
3159:
3151:
3147:
3143:
3139:
3134:
3130:
3126:
3116:
3113:
3109:
3104:
3102:
3101:DNA sequences
3098:
3094:
3090:
3086:
3081:
3079:
3075:
3074:flicker noise
3071:
3067:
3063:
3059:
3055:
3050:
3040:
3038:
3020:
3016:
2995:
2987:
2984:
2977:
2973:
2965:
2956:
2952:
2949:
2946:
2943:
2932:
2928:
2919:
2915:
2908:
2902:
2896:
2882:
2880:
2861:
2831:
2815:
2803:
2797:
2794:
2784:
2780:
2769:
2765:
2762:
2746:
2738:
2734:
2723:
2719:
2716:
2697:
2691:
2685:
2657:
2628:
2607:
2599:
2596:
2589:
2585:
2577:
2571:
2567:
2564:
2561:
2558:
2552:
2549:
2541:
2537:
2530:
2524:
2518:
2498:
2478:
2464:
2456:
2442:
2411:
2369:
2349:
2317:
2311:
2308:
2305:
2299:
2296:
2292:
2287:
2283:
2276:
2260:
2257:
2253:
2248:
2244:
2237:
2221:
2217:
2213:
2210:
2206:
2201:
2197:
2190:
2176:
2156:
2149:
2148:
2133:
2129:
2125:
2118:
2102:
2098:
2093:
2089:
2082:
2066:
2062:
2058:
2054:
2049:
2045:
2038:
2024:
2017:
2016:
2001:
1997:
1993:
1986:
1970:
1966:
1961:
1957:
1950:
1934:
1930:
1926:
1922:
1917:
1913:
1906:
1903:
1902:
1887:
1883:
1879:
1872:
1856:
1852:
1847:
1843:
1836:
1822:
1818:
1814:
1807:
1804:
1803:
1788:
1784:
1780:
1773:
1759:
1755:
1751:
1744:
1728:
1722:
1718:
1711:
1708:
1707:
1689:
1683:
1675:
1658:
1650:
1646:
1637:
1620:
1612:
1608:
1599:
1596:
1595:
1589:
1575:
1572:
1569:
1561:
1545:
1525:
1503:
1499:
1476:
1472:
1462:
1444:
1440:
1436:
1414:
1390:
1386:
1382:
1358:
1355:
1334:
1325:
1323:
1319:
1314:
1301:
1297:
1289:
1286:
1283:
1275:
1271:
1268:
1265:
1258:
1255:
1249:
1245:
1238:
1235:
1232:
1228:
1224:
1219:
1216:
1213:
1209:
1205:
1202:
1196:
1193:
1190:
1184:
1181:
1178:
1172:
1168:
1164:
1160:
1155:
1152:
1148:
1142:
1139:
1134:
1128:
1122:
1114:
1100:
1086:
1077:
1075:
1071:
1067:
1063:
1058:
1055:
1051:
1049:
1045:
1041:
1036:
1034:
1030:
1026:
1018:
1015:
1011:
1006:
998:
989:
987:
983:
979:
975:
971:
970:fractal noise
967:
963:
959:
955:
954:
953:flicker noise
948:
946:
942:
938:
934:
930:
925:
912:
906:
903:
900:
897:
891:
888:
883:
880:
876:
871:
865:
859:
856:
851:
848:
844:
839:
835:
829:
826:
822:
818:
812:
809:
806:
803:
800:
792:
788:
785:
778:
774:
771:
763:
759:
755:
750:
746:
739:
736:
732:
724:
721:
718:
714:
707:
702:
699:
693:
687:
684:
681:
675:
655:
646:
630:
626:
617:
614:
596:
592:
583:
570:
564:
561:
558:
555:
549:
546:
541:
537:
532:
526:
520:
517:
512:
508:
503:
495:
491:
487:
482:
478:
475:
472:
469:
460:
457:
452:
447:
443:
435:
431:
424:
421:
415:
412:
406:
400:
392:
378:
358:
350:
334:
325:
323:
318:
305:
298:
294:
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153:fractal noise
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9968:
9913:Noise figure
9874:Engineering
9863:Worley noise
9828:
9793:Cosmic noise
9716:Human health
9571:
9567:
9520:
9516:
9491:
9485:
9481:
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9450:
9443:Schottky, W.
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8807:the original
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8751:mlab.uiah.fi
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7024:Nano Letters
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6642:November 22,
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6634:
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6503:Crest factor
6450:
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6407:noises, the
6400:
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6331:Taylor's law
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5971:
5966:white matter
5958:cable theory
5923:
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4301:with height
4022:
4018:femtoseconds
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9939:Phase noise
9918:Noise floor
9853:Value noise
9845:White noise
9788:Burst noise
9706:Environment
9701:Electronics
9684:Noise in...
9660:Noise power
8831:: 707–710.
8655:: 141–150.
8244:5 September
6878:SIAM Review
6493:White noise
6455:signal for
6393:phase space
5954:gray matter
5930:ion channel
5002:increases,
4299:square wave
4023:Now we have
3166:hourglasses
3066:resistivity
1676:tot. power
1638:avg. power
1560:Brown noise
1070:loudspeaker
1033:white noise
1017:spectrogram
1010:white noise
992:Description
935:systems in
199:white noise
190:systems in
188:loudspeaker
10270:Categories
10207:2D (Image)
9840:Shot noise
9829:Pink noise
9813:Infrasound
9808:Grey noise
9640:Distortion
9118:References
8869:1511.03393
8862:(4): 108.
8780:2015-11-14
8756:2015-11-14
8540:: 223–243.
8435:1902.00481
8376:1801.02986
8278:1802.00392
8164:(2): 405.
7559:2111.08939
7486:2023-07-26
7436:2023-07-17
6957:2024-02-06
6952:www.sfu.ca
6784:2019-08-08
6548:Statistics
6538:Shot noise
6465:audiophile
6461:headphones
6429:microphone
6300:See also:
5978:psychology
5932:gating to
3720:Note that
3097:heart beat
3083:General 1/
3043:Occurrence
1600:avg. amp.
1597:dimensions
1491:and power
1328:Properties
1322:any number
1080:Generation
1044:Bark scale
962:Mandelbrot
927:General 1/
257:media help
239:normalized
223:Pink noise
205:Definition
132:Pink noise
10286:Acoustics
10133:Acoustics
9696:Buildings
9278:CiteSeerX
9237:CiteSeerX
9066:Soundguys
8993:AE Design
8949:118174242
8924:1404.4076
8649:Physica A
8634:119608542
8609:0708.2053
8462:2160-3308
8403:1367-2630
8344:667085096
8106:1307.4797
8022:0021-8979
7961:(1): 43.
7848:0033-295X
7826:CiteSeerX
7797:145051976
7754:0036-8075
7586:195064621
7505:Epilepsia
7481:243735998
7404:206549862
7388:0036-8075
7363:1305.5869
7323:1476-4687
7052:1530-6984
6595:CiteSeerX
6555:Footnotes
6405:crackling
6347:power law
6327:power law
6102:−
6051:
5986:film shot
5872:−
5868:τ
5864:∝
5858:τ
5846:σ
5825:τ
5802:τ
5790:σ
5760:˙
5728:−
5725:α
5721:τ
5717:∝
5699:σ
5690:−
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5679:≈
5673:τ
5661:σ
5618:α
5614:ω
5596:ω
5578:˙
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5495:∼
5492:ω
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5469:τ
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5431:ω
5422:ω
5404:˙
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5350:∫
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5207:∞
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5176:σ
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5119:σ
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5025:ω
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4842:˙
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4780:≈
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4751:−
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4526:σ
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3991:×
3968:σ
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3840:¯
3821:−
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3763:σ
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3602:τ
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3548:τ
3527:τ
3482:˙
3417:˙
3395:˙
3370:˙
3335:˙
3299:˙
3260:˙
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2947:π
2916:∑
2885:2D signal
2798:
2766:π
2747:−
2720:π
2586:∑
2562:π
2553:
2538:∑
2467:1D signal
2443:σ
2440:‖
2432:‖
2412:μ
2370:σ
2350:μ
2309:−
2306:α
2258:α
2211:α
2177:α
1651:θ
1613:θ
1570:α
1546:α
1526:θ
1504:θ
1477:θ
1407:, and in
1287:−
1269:π
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1236:−
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860:χ
857:∼
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700:σ
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565:π
547:∼
538:ϕ
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509:χ
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473:π
461:
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432:∑
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173:frequency
117:grayscale
10167:Denoise
9547:14339595
9484:noise".
9445:(1922).
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9394:Archived
9308:14973015
9300:11396846
9179:noise".
9160:10035754
9128:Noise".
8803:Preprint
8519:22304168
8311:52243763
8303:30240245
8239:YaleNews
8218:17 April
8198:38257498
8189:10821460
8139:16030927
8131:23912107
7914:noise".
7856:11212631
7814:Noise".
7705:Archived
7644:13678372
7535:22967005
7396:23970562
7276:37302662
7109:10035754
7077:Noise".
7060:25942441
6775:Archived
6719:24505215
6711:11508842
6471:See also
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6362:sandpile
6292:<1).
6249:, where
5946:epilepsy
3148:, where
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982:Brownian
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10169:methods
10074:,
9628:General
9461:Bibcode
9423:Bibcode
9386:Bibcode
9327:Bibcode
9259:3430225
9229:Bibcode
9191:Bibcode
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8929:Bibcode
8896:2388285
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8733:9908765
8713:Bibcode
8657:Bibcode
8614:Bibcode
8581:4263093
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8499:Bibcode
8440:Bibcode
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8062:Bibcode
8002:Bibcode
7963:Bibcode
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6253:is the
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5950:seizure
3062:neurons
3035:is the
2877:is the
2424:and sd
2362:and sd
1558:(e.g.:
1048:loudest
943:driven
171:to the
140:⁄
10236:(BM3D)
9958:Ratios
9818:Jitter
9769:(AWGN)
9721:Images
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5920:Humans
4352:. Let
4185:where
3940:where
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3008:where
2844:where
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47:Purple
10281:Sound
10247:(DAE)
10044:SINAD
9994:dBrnC
9935:(NVH)
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9736:Ships
9731:Rooms
9726:Radio
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9620:Noise
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9543:S2CID
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9397:(PDF)
9374:(PDF)
9304:S2CID
9215:(PDF)
9164:S2CID
8945:S2CID
8919:arXiv
8892:S2CID
8864:arXiv
8810:(PDF)
8799:(PDF)
8684:arXiv
8630:S2CID
8604:arXiv
8577:S2CID
8487:(PDF)
8430:arXiv
8371:arXiv
8307:S2CID
8273:arXiv
8135:S2CID
8101:arXiv
8036:Noise
7793:S2CID
7666:(PDF)
7582:S2CID
7554:arXiv
7477:S2CID
7400:S2CID
7358:arXiv
7327:S2CID
7272:S2CID
7199:S2CID
7113:S2CID
6778:(PDF)
6767:(PDF)
6715:S2CID
6575:(PDF)
6269:with
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3974:25000
3356:, so
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32:White
10101:SQNR
10091:SINR
9533:ISBN
9356:ISBN
9296:PMID
9255:PMID
9156:PMID
9073:2022
9030:2022
9000:2022
8968:ISBN
8729:PMID
8515:PMID
8458:ISSN
8399:ISSN
8340:OCLC
8330:ISBN
8299:PMID
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8220:2014
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8127:PMID
8018:ISSN
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7844:ISSN
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7750:ISSN
7640:PMID
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6740:ISBN
6707:PMID
6666:ISBN
6644:2022
6613:PMID
6403:and
6383:, 1/
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5936:and
5522:For
3750:The
3054:tide
1588:):
1562:has
1320:or
1068:and
1038:The
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243:dBFS
52:Grey
37:Pink
10111:CNR
10076:SNR
10034:MER
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9431:doi
9419:362
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8882:doi
8829:300
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8557:189
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6375:In
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5976:in
5942:LFP
5938:MEG
5934:EEG
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2809:max
2795:log
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