Colors of noise

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Colors of noise
White
Pink
Red (Brownian)
Purple
Grey

In audio engineering, electronics, physics, and many other fields, the color of noise refers to the power spectrum of a noise signal (a signal produced by a stochastic process). Different colors of noise have significantly different properties. For example, as audio signals they will sound different to human ears, and as images they will have a visibly different texture. Therefore, each application typically requires noise of a specific color. This sense of 'color' for noise signals is similar to the concept of timbre in music (which is also called "tone color"[ citation needed ]); however, the latter is almost always used for sound, and may consider very detailed features of the spectrum.

Contents

The practice of naming kinds of noise after colors started with white noise, a signal whose spectrum has equal power within any equal interval of frequencies. That name was given by analogy with white light, which was (incorrectly) assumed to have such a flat power spectrum over the visible range.[ citation needed ] Other color names, such as pink, red, and blue were then given to noise with other spectral profiles, often (but not always) in reference to the color of light with similar spectra. Some of those names have standard definitions in certain disciplines, while others are very informal and poorly defined. Many of these definitions assume a signal with components at all frequencies, with a power spectral density per unit of bandwidth proportional to 1/f β and hence they are examples of power-law noise. For instance, the spectral density of white noise is flat (β = 0), while flicker or pink noise has β = 1, and Brownian noise has β = 2.

Simulated power spectral densities as a function of frequency for various colors of noise (violet, blue, white, pink, brown/red). The power spectral densities are arbitrarily normalized such that the value of the spectra are approximately equivalent near 1 kHz. Note the slope of the power spectral density for each spectrum provides the context for the respective electromagnetic/color analogy. The Colors of Noise.png
Simulated power spectral densities as a function of frequency for various colors of noise (violet, blue, white, pink, brown/red). The power spectral densities are arbitrarily normalized such that the value of the spectra are approximately equivalent near 1 kHz. Note the slope of the power spectral density for each spectrum provides the context for the respective electromagnetic/color analogy.

Technical definitions

Various noise models are employed in analysis, many of which fall under the above categories. AR noise or "autoregressive noise" is such a model, and generates simple examples of the above noise types, and more. The Federal Standard 1037C Telecommunications Glossary [1] [2] defines white, pink, blue, and black.

The color names for these different types of sounds are derived from a loose analogy between the spectrum of frequencies of sound wave present in the sound (as shown in the blue diagrams) and the equivalent spectrum of light wave frequencies. That is, if the sound wave pattern of "blue noise" were translated into light waves, the resulting light would be blue, and so on.[ citation needed ]

White noise

White noise spectrum. Flat power spectrum.
(logarithmic frequency axis) White noise spectrum.svg
White noise spectrum. Flat power spectrum.
(logarithmic frequency axis)

White noise is a signal (or process), named by analogy to white light, with a flat frequency spectrum when plotted as a linear function of frequency (e.g., in Hz). In other words, the signal has equal power in any band of a given bandwidth (power spectral density) when the bandwidth is measured in Hz. For example, with a white noise audio signal, the range of frequencies between 40 Hz and 60 Hz contains the same amount of sound power as the range between 400 Hz and 420 Hz, since both intervals are 20 Hz wide. Note that spectra are often plotted with a logarithmic frequency axis rather than a linear one, in which case equal physical widths on the printed or displayed plot do not all have the same bandwidth, with the same physical width covering more Hz at higher frequencies than at lower frequencies. In this case a white noise spectrum that is equally sampled in the logarithm of frequency (i.e., equally sampled on the X axis) will slope upwards at higher frequencies rather than being flat. However it is not unusual in practice for spectra to be calculated using linearly-spaced frequency samples but plotted on a logarithmic frequency axis, potentially leading to misunderstandings and confusion if the distinction between equally spaced linear frequency samples and equally spaced logarithmic frequency samples is not kept in mind. [3]

Pink noise

Pink noise spectrum. Power density falls off at 10 dB/decade (-3.01 dB/octave). Pink noise spectrum.svg
Pink noise spectrum. Power density falls off at 10 dB/decade (−3.01 dB/octave).

The frequency spectrum of pink noise is linear in logarithmic scale; it has equal power in bands that are proportionally wide. [4] This means that pink noise would have equal power in the frequency range from 40 to 60 Hz as in the band from 4000 to 6000 Hz. Since humans hear in such a proportional space, where a doubling of frequency (an octave) is perceived the same regardless of actual frequency (40–60 Hz is heard as the same interval and distance as 4000–6000 Hz), every octave contains the same amount of energy and thus pink noise is often used as a reference signal in audio engineering. The spectral power density, compared with white noise, decreases by 3.01 dB per octave (density proportional to 1/f ). For this reason, pink noise is often called "1/f noise".

Since there are an infinite number of logarithmic bands at both the low frequency (DC) and high frequency ends of the spectrum, any finite energy spectrum must have less energy than pink noise at both ends. Pink noise is the only power-law spectral density that has this property: all steeper power-law spectra are finite if integrated to the high-frequency end, and all flatter power-law spectra are finite if integrated to the DC, low-frequency limit.[ citation needed ]

Brownian noise

Brown spectrum (-6.02 dB/octave) Brown noise spectrum.svg
Brown spectrum (−6.02 dB/octave)

Brownian noise, also called Brown noise, is noise with a power density which decreases 6.02 dB per octave with increasing frequency (frequency density proportional to 1/f2) over a frequency range excluding zero (DC).

Brownian noise can be generated with temporal integration of white noise. "Brown" noise is not named for a power spectrum that suggests the color brown; rather, the name derives from Brownian motion. Also known as "random walk" or "drunkard's walk". "Red noise" describes the shape of the power spectrum, with pink being between red and white.

Blue noise

Blue spectrum (+3.01 dB/octave) Blue noise spectrum.svg
Blue spectrum (+3.01 dB/octave)

Blue noise is also called azure noise. Blue noise's power density increases 3.01 dB per octave with increasing frequency (density proportional to f ) over a finite frequency range. [5] In computer graphics, the term "blue noise" is sometimes used more loosely as any noise with minimal low frequency components and no concentrated spikes in energy. This can be good noise for dithering. [6] Retinal cells are arranged in a blue-noise-like pattern which yields good visual resolution. [6] [7]

Cherenkov radiation is a naturally occurring example of almost perfect blue noise, with the power density growing linearly with frequency over spectrum regions where the permeability of index of refraction of the medium are approximately constant. The exact density spectrum is given by the Frank–Tamm formula. In this case, the finiteness of the frequency range comes from the finiteness of the range over which a material can have a refractive index greater than unity. Cherenkov radiation also appears as a bright blue color, for these reasons.

Violet noise

Violet spectrum (+6.02 dB/octave) Violet noise spectrum.svg
Violet spectrum (+6.02 dB/octave)

Violet noise is also called purple noise. Violet noise's power density increases 6.02 dB per octave with increasing frequency [8] [9] (density proportional to f 2) over a finite frequency range. It is also known as differentiated white noise, due to its being the result of the differentiation of a white noise signal.

Due to the diminished sensitivity of the human ear to high-frequency hiss and the ease with which white noise can be electronically differentiated (high-pass filtered at first order), many early adaptations of dither to digital audio used violet noise as the dither signal.[ citation needed ]

Acoustic thermal noise of water has a violet spectrum, causing it to dominate hydrophone measurements at high frequencies. [10] [11]

Grey noise

Grey spectrum Gray noise spectrum.svg
Grey spectrum

Grey noise is random white noise subjected to a psychoacoustic equal loudness curve (such as an inverted A-weighting curve) over a given range of frequencies, giving the listener the perception that it is equally loud at all frequencies.[ citation needed ] This is in contrast to standard white noise which has equal strength over a linear scale of frequencies but is not perceived as being equally loud due to biases in the human equal-loudness contour.

Informal definitions

There are also many colors used without precise definitions (or as synonyms for formally defined colors), sometimes with multiple definitions.

Red noise

Green noise

Black noise

Noisy white

In telecommunication, the term noisy white has the following meanings: [19]

Noisy black

In telecommunication, the term noisy black has the following meanings: [20]

See also

Related Research Articles

Bandwidth (signal processing) Difference between the upper and lower frequencies passed by a filter, communication channel, or signal spectrum

Bandwidth is the difference between the upper and lower frequencies in a continuous band of frequencies. It is typically measured in hertz, and depending on context, may specifically refer to passband bandwidth or baseband bandwidth. Passband bandwidth is the difference between the upper and lower cutoff frequencies of, for example, a band-pass filter, a communication channel, or a signal spectrum. Baseband bandwidth applies to a low-pass filter or baseband signal; the bandwidth is equal to its upper cutoff frequency.

Color Characteristic of human visual perception

Color, or colour, is the characteristic of visual perception described through color categories, with names such as red, orange, yellow, green, blue, or purple. This perception of color derives from the stimulation of photoreceptor cells by electromagnetic radiation. Color categories and physical specifications of color are associated with objects through the wavelengths of the light that is reflected from them and their intensities. This reflection is governed by the object's physical properties such as light absorption, emission spectra, etc.

The decibel is a relative unit of measurement corresponding to one tenth of a bel (B). It is used to express the ratio of one value of a power or root-power quantity to another, on a logarithmic scale. A logarithmic quantity in decibels is called a level. Two signals whose levels differ by one decibel have a power ratio of 101/10 or root-power ratio of 10120.

Spectrum Continuous range of values, such as wavelengths in physics

A spectrum is a condition that is not limited to a specific set of values but can vary, without steps, across a continuum. The word was first used scientifically in optics to describe the rainbow of colors in visible light after passing through a prism. As scientific understanding of light advanced, it came to apply to the entire electromagnetic spectrum.

Phase noise

In signal processing, phase noise is the frequency-domain representation of random fluctuations in the phase of a waveform, corresponding to time-domain deviations from perfect periodicity ("jitter"). Generally speaking, radio-frequency engineers speak of the phase noise of an oscillator, whereas digital-system engineers work with the jitter of a clock.

Wiens displacement law

Wien's displacement law states that the black-body radiation curve for different temperatures will peak at different wavelengths that are inversely proportional to the temperature. The shift of that peak is a direct consequence of the Planck radiation law, which describes the spectral brightness of black-body radiation as a function of wavelength at any given temperature. However, it had been discovered by Wilhelm Wien several years before Max Planck developed that more general equation, and describes the entire shift of the spectrum of black-body radiation toward shorter wavelengths as temperature increases.

White noise Random signal having equal intensity at different frequencies, giving it a constant power spectral density

In signal processing, white noise is a random signal having equal intensity at different frequencies, giving it a constant power spectral density. The term is used, with this or similar meanings, in many scientific and technical disciplines, including physics, acoustical engineering, telecommunications, and statistical forecasting. White noise refers to a statistical model for signals and signal sources, rather than to any specific signal. White noise draws its name from white light, although light that appears white generally does not have a flat power spectral density over the visible band.

Pink noise or 1f noise is a signal or process with a frequency spectrum such that the power spectral density is inversely proportional to the frequency of the signal. In pink noise, each octave interval carries an equal amount of noise energy.

In information theory, the Shannon–Hartley theorem tells the maximum rate at which information can be transmitted over a communications channel of a specified bandwidth in the presence of noise. It is an application of the noisy-channel coding theorem to the archetypal case of a continuous-time analog communications channel subject to Gaussian noise. The theorem establishes Shannon's channel capacity for such a communication link, a bound on the maximum amount of error-free information per time unit that can be transmitted with a specified bandwidth in the presence of the noise interference, assuming that the signal power is bounded, and that the Gaussian noise process is characterized by a known power or power spectral density. The law is named after Claude Shannon and Ralph Hartley.

Spectral density Relative importance of certain frequencies in a composite signal

The power spectrum of a time series describes the distribution of power into frequency components composing that signal. According to Fourier analysis, any physical signal can be decomposed into a number of discrete frequencies, or a spectrum of frequencies over a continuous range. The statistical average of a certain signal or sort of signal as analyzed in terms of its frequency content, is called its spectrum.

Dominant wavelength any monochromatic spectral light that evokes the corresponding opposite perception of hue

In color science, the dominant wavelength are ways of characterizing any light mixture in terms of the monochromatic spectral light that evokes an identical perception of hue. For a given physical light mixture, the dominant and complementary wavelengths are not entirely fixed, but vary according to the illuminating light's precise color, called the white point, due to the color constancy of vision.

Spectral color Color evoked by a single wavelength of light in the visible spectrum

A spectral color is a color that is evoked in a typical human by a single wavelength of light in the visible spectrum, or by a relatively narrow band of wavelengths, also known as monochromatic light. Every wavelength of visible light is perceived as a spectral color, in a continuous spectrum; the colors of sufficiently close wavelengths are indistinguishable for the human eye.

Brownian noise The kind of signal noise produced by Brownian motion

In science, Brownian noise, also known as Brown noise or red noise, is the kind of signal noise produced by Brownian motion, hence its alternative name of random walk noise. The term "Brown noise" does not come from the color, but after Robert Brown, who documented the erratic motion for multiple types of inanimate particles in water. The term "red noise" comes from the "white noise"/"white light" analogy; red noise is strong in longer wavelengths, similar to the red end of the visible spectrum.

<i>E</i><sub>b</sub>/<i>N</i><sub>0</sub>

In digital communication or data transmission, Eb/N0 is a normalized signal-to-noise ratio (SNR) measure, also known as the "SNR per bit". It is especially useful when comparing the bit error rate (BER) performance of different digital modulation schemes without taking bandwidth into account.

Noise (electronics) Random fluctuation in an electrical signal

In electronics, noise is an unwanted disturbance in an electrical signal. Noise generated by electronic devices varies greatly as it is produced by several different effects.

Grey noise Random noise

Grey noise is random noise whose frequency spectrum follows a psychoacoustic equal loudness curve.

Flicker noise is a type of electronic noise with a 1/f power spectral density. It is therefore often referred to as 1/f noise or pink noise, though these terms have wider definitions. It occurs in almost all electronic devices and can show up with a variety of other effects, such as impurities in a conductive channel, generation and recombination noise in a transistor due to base current, and so on.

In communications, noise spectral density, noise power density, noise power spectral density, or simply noise density (N0) is the power spectral density of noise or the noise power per unit of bandwidth. It has dimension of power over frequency, whose SI unit is watt per hertz. It is commonly used in link budgets as the denominator of the important figure-of-merit ratios, such as carrier-to-noise-density ratio as well as Eb/N0 and Es/N0.

In statistical signal processing, the goal of spectral density estimation (SDE) is to estimate the spectral density of a random signal from a sequence of time samples of the signal. Intuitively speaking, the spectral density characterizes the frequency content of the signal. One purpose of estimating the spectral density is to detect any periodicities in the data, by observing peaks at the frequencies corresponding to these periodicities.

Noise refers to many types of random or unwanted signals, most commonly acoustic noise, but also including the following:

References

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  2. "Federal Standard 1037C". Institute for Telecommunication Sciences. Institute for Telecommunication Sciences, National Telecommunications and Information Administration (ITS-NTIA). Retrieved 16 January 2018.
  3. R. D. Peters, 2012
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  5. "Definition: blue noise". www.its.bldrdoc.gov.
  6. 1 2 Mitchell, Don P., "Generating Antialiased Images at Low Sampling Densities." Computer Graphics, volume 21, number 4, July 1987.
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  8. Transactions of the American Society of Heating, Refrigerating and Air-Conditioning Engineers 1968 Quote: 'A "purple noise," accordingly, is a noise the spectrum level of which rises with frequency.'
  9. Estimating double difference GPS multipath under kinematicconditions. Zhang, Q.J. and Schwarz, K.-P.. Position Location and Navigation Symposium, pp. 285–91. Apr 1996. 10.1109/PLANS.1996.509090 "The spectral analysis shows that GPS acceleration errors seem to be violet noise processes. They are dominated by high-frequency noise."
  10. Anthropogenic and natural sources of ambient noise in the ocean doi : 10.3354/meps08353 "Predictions of the thermal noise spectrum, derived from classical statistical mechanics, suggest increasing noise with frequency with a positive slope of 6.02 dB octave−1" "Note that thermal noise increases at the rate of 20 dB decade−1"
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  15. Lau, Daniel Leo; Arce, Gonzalo R.; Gallagher, Neal C. (1998), "Green-noise digital halftoning", Proceedings of the IEEE, 86 (12): 2424–42, doi:10.1109/5.735449
  16. 1 2 Joseph S. Wisniewski (7 October 1996). "Colors of noise pseudo FAQ, version 1.3". Newsgroup:  comp.dsp. Archived from the original on 30 April 2011. Retrieved 1 March 2011.
  17. Schroeder, Manfred (2009). Fractals, Chaos, Power Laws: Minutes from an Infinite Paradise. Courier Dover. pp. 129–30. ISBN   978-0486472041.
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  19. "Definition: noisy white". www.its.bldrdoc.gov.
  20. "Definition: noisy black". www.its.bldrdoc.gov.

PD-icon.svg This article incorporates  public domain material from the General Services Administration document: "Federal Standard 1037C".