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Noise

Noise is sound, chiefly unwanted, unintentional, or harmful sound considered unpleasant, loud, or disruptive to mental or hearing faculties. From a physics standpoint, there is no distinction between noise and desired sound, as both are vibrations through a medium, such as air or water. The difference arises when the brain receives and perceives a sound.

Acoustic noise is any sound in the acoustic domain, either deliberate (e.g., music or speech) or unintended. In contrast, noise in electronics may not be audible to the human ear and may require instruments for detection.

In audio engineering, noise can refer to the unwanted residual electronic noise signal that gives rise to acoustic noise heard as a hiss. This signal noise is commonly measured using A-weighting or ITU-R 468 weighting.

In experimental sciences, noise can refer to any random fluctuations of data that hinders perception of a signal.

Measurement
Sound is measured based on the amplitude and frequency of a sound wave. Amplitude measures how forceful the wave is. The energy in a sound wave is measured in decibels (dB), the measure of loudness, or intensity of a sound; this measurement describes the amplitude of a sound wave. Decibels are expressed in a logarithmic scale. On the other hand, pitch describes the frequency of a sound and is measured in hertz (Hz).

The main instrument to measure sounds in the air is the Sound Level Meter. There are many different varieties of instruments that are used to measure noise - Noise Dosimeters are often used in occupational environments, noise monitors are used to measure environmental noise and noise pollution, and recently smartphone-based sound level meter applications (apps) are being used to crowdsource and map recreational and community noise.

A-weighting is applied to a sound spectrum to represent the sound that humans are capable of hearing at each frequency. Sound pressure is thus expressed in terms of dBA. 0 dBA is the softest level that a person can hear. Normal speaking voices are around 65 dBA. A rock concert can be about 120 dBA.

Recording and reproduction
In audio, recording, and broadcast systems, audio noise refers to the residual low-level sound (four major types: hiss, rumble, crackle, and hum) that is heard in quiet periods of program. This variation from the expected pure sound or silence can be caused by the audio recording equipment, the instrument, or ambient noise in the recording room.

In audio engineering it can refer either to the acoustic noise from loudspeakers or to the unwanted residual electronic noise signal that gives rise to acoustic noise heard as hiss. This signal noise is commonly measured using A-weighting or ITU-R 468 weighting

Noise is often generated deliberately and used as a test signal for audio recording and reproduction equipment.

Environmental noise
Environmental noise is the accumulation of all noise present in a specified environment. The principal sources of environmental noise are surface motor vehicles, aircraft, trains and industrial sources. These noise sources expose millions of people to noise pollution that creates not only annoyance, but also significant health consequences such as elevated incidence of hearing loss, cardiovascular disease, and many others. Urban noise is generally not of an intensity that causes hearing loss but it interrupts sleep, disturbs communication and interferes with other human activities. There are a variety of mitigation strategies and controls available to reduce sound levels including source intensity reduction, land-use planning strategies, noise barriers and sound baffles, time of day use regimens, vehicle operational controls and architectural acoustics design measures.

Regulation
Certain geographic areas or specific occupations may be at a higher risk of being exposed to constantly high levels of noise; regulation may prevent negative health outcomes. Noise regulation includes statutes or guidelines relating to sound transmission established by national, state or provincial and municipal levels of government. Environmental noise is governed by laws and standards which set maximum recommended levels of noise for specific land uses, such as residential areas, areas of outstanding natural beauty, or schools. These standards usually specify measurement using a weighting filter, most often A-weighting.

United States
In 1972, the Noise Control Act was passed to promote a healthy living environment for all Americans, where noise does not pose a threat to human health. This policy's main objectives were: (1) establish coordination of research in the area of noise control, (2) establish federal standards on noise emission for commercial products, and (3) promote public awareness about noise emission and reduction.

The Quiet Communities Act of 1978 promotes noise control programs at the state and local level and developed a research program on noise control. Both laws authorized the Environmental Protection Agency to study the effects of noise and evaluate regulations regarding noise control.

The National Institute for Occupational Safety and Health (NIOSH) provides recommendation on noise exposure in the workplace. In 1972 (revised in 1998), NIOSH published a document outlining recommended standards relating to the occupational exposure to noise, with the purpose of reducing the risk of developing permanent hearing loss related to exposure at work. This publication set the recommended exposure limit (REL) of noise in an occupation setting to 85 dBA for 8 hours using a 3-dB exchange rate (every 3-dB increase in level, duration of exposure should be cut in half, i.e., 88 dBA for 4 hours, 91 dBA for 2 hours, 94 dBA for 1 hour, etc.). However, in 1973 the Occupational Safety and Health Administration (OSHA) maintained the requirement of an 8-hour average of 90 dBA. The following year, OSHA required employers to provide a hearing conservation program to workers exposed to 85 dBA average 8-hour workdays.

Europe
The European Environment Agency regulates noise control and surveillance within the European Union. The Environmental Noise Directive was set to determine levels of noise exposure, increase public access to information regarding environmental noise, and reduce environmental noise. Additionally, in the European Union, underwater noise is a pollutant according to the Marine Strategy Framework Directive (MSFD). The MSFD requires EU Member States to achieve or maintain Good Environmental Status, meaning that the "introduction of energy, including underwater noise, is at levels that do not adversely affect the marine environment".

Health effects
Exposure to noise is associated with several negative health outcomes. Depending on duration and level of exposure, noise may cause or increase the likelihood of hearing loss, high blood pressure, ischemic heart disease, sleep disturbances, injuries, and even decreased school performance. When noise is prolonged, the body's stress responses can be triggered; which can include increased heartbeat, and rapid breathing. There are also causal relationships between noise and psychological effects such as annoyance, psychiatric disorders, and effects on psychosocial well-being.

Noise exposure has increasingly been identified as a public health issue, especially in an occupational setting, as demonstrated with the creation of NIOSH's Noise and Hearing Loss Prevention program. Noise has also proven to be an occupational hazard, as it is the most common work-related pollutant. Noise-induced hearing loss, when associated with noise exposure at the workplace is also called occupational hearing loss. For example, some occupational studies have shown a relation between those who are regularly exposed to noise above 85 decibels to have higher blood pressure than those who are not exposed.

Hearing loss prevention
While noise-induced hearing loss is permanent, it is also preventable. Particularly in the workplace, regulations may exist limiting permissible exposure limit to noise. This can be especially important for professionals working in settings with consistent exposure to loud sounds, such as musicians, music teachers and audio engineers. Examples of measures taken to prevent noise-induced hearing loss in the workplace include engineering noise control, the Buy-Quiet initiative, creation of the Safe-In-Sound award, and noise surveillance.

OSHA requires the use of hearing protection. But the HPD (without individual selection, training and fit testing) does not significantly reduce the risk of hearing loss. For example, one study covered more than 19 thousand workers, some of whom usually used hearing protective devices, and some did not use them at all. There was no statistically significant difference in the risk of noise-induced hearing loss.

Literary views
Roland Barthes distinguishes between physiological noise, which is merely heard, and psychological noise, which is actively listened to. Physiological noise is felt subconsciously as the vibrations of the noise (sound) waves physically interact with the body while psychological noise is perceived as our conscious awareness shifts its attention to that noise.

Luigi Russolo, one of the first composers of noise music, wrote the essay The Art of Noises. He argued that any kind of noise could be used as music, as audiences become more familiar with noises caused by technological advancements; noise has become so prominent that pure sound no longer exists.

Avant-garde composer Henry Cowell claimed that technological advancements have reduced unwanted noises from machines, but have not managed so far to eliminate them.

Felix Urban sees noise as a result of cultural circumstances. In his comparative study on sound and noise in cities, he points out that noise regulations are only one indicator of what is considered as harmful. It is the way in which people live and behave (acoustically) that determines the way how sounds are perceived.

title: Noise


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Noise-equivalent power

Noise-equivalent power (NEP) is a measure of the sensitivity of a photodetector or detector system. It is defined as the signal power that gives a signal-to-noise ratio of one in a one hertz output bandwidth. An output bandwidth of one hertz is equivalent to half a second of integration time. The units of NEP are watts per square root hertz. The NEP is equal to the noise amplitude spectral density (expressed in units of $$\mathrm{A}/\sqrt{\mathrm{Hz}}$$ or $$\mathrm{V}/\sqrt{\mathrm{Hz}}$$) divided by the responsivity (expressed in units of $$\mathrm{A}/\mathrm{W}$$ or $$\mathrm{V}/\mathrm{W}$$, respectively). The fundamental equation is $$SNR = P/NEP$$.

A smaller NEP corresponds to a more sensitive detector. For example, a detector with an NEP of $$10^{-12} \mathrm{W}/\sqrt{\mathrm{Hz}}$$ can detect a signal power of one picowatt with a signal-to-noise ratio (SNR) of one after one half second of averaging. The SNR improves as the square root of the averaging time, and hence the SNR in this example can be improved by a factor of 10 by averaging 100-times longer, i.e. for 50 seconds.

If the NEP refers to the signal power absorbed in the detector, it is known as the electrical NEP. If instead it refers to the signal power incident on the detector system, it is called the optical NEP. The optical NEP is equal to the electrical NEP divided by the optical coupling efficiency of the detector system.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Noise-equivalent power


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Noise figure

Noise figure (NF) and noise factor (F) are figures of merit that indicate degradation of the signal-to-noise ratio (SNR) that is caused by components in a signal chain. These figures of merit are used to evaluate the performance of an amplifier or a radio receiver, with lower values indicating better performance.

The noise factor is defined as the ratio of the output noise power of a device to the portion thereof attributable to thermal noise in the input termination at standard noise temperature T0 (usually 290 K). The noise factor is thus the ratio of actual output noise to that which would remain if the device itself did not introduce noise, which is equivalent to the ratio of input SNR to output SNR.

The noise factor and noise figure are related, with the former being a unitless ratio and the latter being the logarithm of the noise factor, expressed in units of decibels (dB).

General
The noise figure is the difference in decibel (dB) between the noise output of the actual receiver to the noise output of an "ideal" receiver with the same overall gain and bandwidth when the receivers are connected to matched sources at the standard noise temperature T0 (usually 290 K). The noise power from a simple load is equal to kTB, where k is the Boltzmann constant, T is the absolute temperature of the load (for example a resistor), and B is the measurement bandwidth.

This makes the noise figure a useful figure of merit for terrestrial systems, where the antenna effective temperature is usually near the standard 290 K. In this case, one receiver with a noise figure, say 2 dB better than another, will have an output signal-to-noise ratio that is about 2 dB better than the other. However, in the case of satellite communications systems, where the receiver antenna is pointed out into cold space, the antenna effective temperature is often colder than 290 K. In these cases a 2 dB improvement in receiver noise figure will result in more than a 2 dB improvement in the output signal-to-noise ratio. For this reason, the related figure of effective noise temperature is therefore often used instead of the noise figure for characterizing satellite-communication receivers and low-noise amplifiers.

In heterodyne systems, output noise power includes spurious contributions from image-frequency transformation, but the portion attributable to thermal noise in the input termination at standard noise temperature includes only that which appears in the output via the principal frequency transformation of the system and excludes that which appears via the image frequency transformation.

Definition
The noise factor $F$ of a system is defined as

where $SNR_{i}$ and $SNR_{o}$ are the input and output signal-to-noise ratios respectively. The $SNR$ quantities are unitless power ratios. Note that this specific definition is only valid for an input signal of which the noise is Ni=kT0B.

The noise figure $NF$ is defined as the noise factor in units of decibels (dB):

where $SNR_{i, dB}$ and $SNR_{o, dB}$ are in units of (dB). These formulae are only valid when the input termination is at standard noise temperature $T_{0} = 290 K$, although in practice small differences in temperature do not significantly affect the values.

The noise factor of a device is related to its noise temperature $T_{e}$:
 * $$F = 1 + \frac{T_\text{e}}{T_0}.$$

Attenuators have a noise factor $T_{e} = T_{0}(F − 1)$ equal to their attenuation ratio $F$ when their physical temperature equals $L$. More generally, for an attenuator at a physical temperature $T_{0}$, the noise temperature is $T$, giving a noise factor
 * $$F = 1 + \frac{(L - 1)T}{T_0}.$$

Noise factor of cascaded devices
If several devices are cascaded, the total noise factor can be found with Friis' formula:
 * $$F = F_1 + \frac{F_2 - 1}{G_1} + \frac{F_3 - 1}{G_1 G_2} + \frac{F_4 - 1}{G_1 G_2 G_3} + \cdots + \frac{F_n - 1}{G_1 G_2 G_3 \cdots G_{n-1}},$$

where $T_{e} = (L − 1)T$ is the noise factor for the $F_{n}$-th device, and $n$ is the power gain (linear, not in dB) of the $G_{n}$-th device. The first amplifier in a chain usually has the most significant effect on the total noise figure because the noise figures of the following stages are reduced by stage gains. Consequently, the first amplifier usually has a low noise figure, and the noise figure requirements of subsequent stages is usually more relaxed.

Noise factor as a function of additional noise
The noise factor may be expressed as a function of the additional output referred noise power $$N_a$$ and the power gain $$G$$ of an amplifier.

Derivation
From the definition of noise factor

 * $$F = \frac{\mathrm{SNR}_\text{i}}{\mathrm{SNR}_\text{o}}=\frac{\frac{S_i}{N_i}}{\frac{S_o}{N_o}},$$

and assuming a system which has a noisy single stage amplifier. The signal to noise ratio of this amplifier would include its own output referred noise $$N_a$$, the amplified signal $$S_iG$$ and the amplified input noise $$N_iG$$,

 * $$\frac{S_o}{N_o}=\frac{S_iG}{N_a+N_iG}$$

Substituting the output SNR to the noise factor definition,

 * $$F = \frac{\frac{S_i}{N_i}}{\frac{S_iG}{N_a+N_iG}}=\frac{N_a+N_iG}{N_iG} = 1 + \frac{N_a}{N_iG}$$

In cascaded systems $$N_i$$ does not refer to the output noise of the previous component. An input termination at the standard noise temperature is still assumed for the individual component. This means that the additional noise power added by each component is independent of the other components.

Optical noise figure
The above describes noise in electrical systems. The optical noise figure is discussed in multiple sources. Electric sources generate noise with a power spectral density, or energy per mode, equal to $n$, where $kT$ is the Boltzmann constant and $k$ is the absolute temperature. One mode has two quadratures, i.e. the amplitudes of $T$$$\mathrm{\omega}t$$ and $cos$$$\mathrm{\omega}t$$ oscillations of voltages, currents or fields. However, there is also noise in optical systems. In these, the sources have no fundamental noise. Instead the energy quantization causes notable shot noise in the detector. In an optical receiver which can output one available mode or two available quadratures this corresponds to a noise power spectral density, or energy per mode, of $sin$ where $hf$ is the Planck constant and $h$ is the optical frequency. In an optical receiver with only one available quadrature the shot noise has a power spectral density, or energy per mode, of only $f$.

In the 1990s, an optical noise figure has been defined. This has been called $hf/2$ for photon number fluctuations. The powers needed for SNR and noise factor calculation are the electrical powers caused by the current in a photodiode. SNR is the square of mean photocurrent divided by variance of photocurrent. Monochromatic or sufficiently attenuated light has a Poisson distribution of detected photons. If, during a detection interval the expectation value of detected photons is $F_{pnf}$ then the variance is also $n$ and one obtains $n$ = $SNR_{pnf,in}$ = $n^{2}/n$. Behind an optical amplifier with power gain $n$ there will be a mean of $G$ detectable signal photons. In the limit of large $Gn$ the variance of photons is $n$ where $Gn(2n_{sp}(G-1)+1)$ is the spontaneous emission factor. One obtains $n_{sp}$ = $SNR_{pnf,out}$ = $G^{2}n^{2}/(Gn(2n_{sp}(G-1)+1))$. Resulting optical noise factor is $n/(2n_{sp}(1-1/G)+1/G)$ = $F_{pnf}$ = $SNR_{pnf,in} / SNR_{pnf,out}$.

$2n_{sp}(1-1/G)+1/G$ is in conceptual conflict with the electrical noise factor, which is now called $F_{pnf}$:

Photocurrent $F_{e}$ is proportional to optical power $I$. $P$ is proportional to squares of a field amplitude (electric or magnetic). So, the receiver is nonlinear in amplitude. The "Power" needed for $P$ calculation is proportional to the 4th power of the signal amplitude. But for $SNR_{pnf}$ in the electrical domain the power is proportional to the square of the signal amplitude.

If $F_{e}$ is a noise factor then its definition must be independent of measurement apparatus and frequency. Consider the signal "Power" in the sense of $SNR_{pnf}$ definition. Behind an amplifier it is proportional to $SNR_{pnf}$. We may replace the photodiode by a thermal power meter, and measured photocurrent $G^{2}n^{2}$ by measured temperature change $$\mathrm{\Delta\theta}$$. "Power", being proportional to $I$ or $I^{2}$, is also proportional to $$(\mathrm{\Delta\theta})$$$P^{2}$. Thermal power meters can be built at all frequencies. Hence it is possible to lower the frequency from optical (say 200 THz) to electrical (say 200 MHz). Still there, "Power" must be proportional to $$(\mathrm{\Delta\theta})$$$^{2}$ or $^{2}$. Electrical power $P^{2}$ is proportional to the square $P$ of voltage $U^{2}$. But "Power" is proportional to $U$.

These implications are in obvious conflict with ~150 years of physics. They are compelling consequence of calling $U^{4}$ a noise factor, or noise figure when expressed in dB.

At any given electrical frequency, noise occurs in both quadratures, i.e. in phase (I) and in quadrature (Q) with the signal. Both these quadratures are available behind the electrical amplifier. The same holds in an optical amplifier. But the direct detection photoreceiver needed for measurement of $F_{pnf}$ takes mainly the in-phase noise into account whereas quadrature noise can be neglected for high $SNR_{pnf}$. Also, the receiver outputs only one baseband signal, corresponding to quadrature. So, one quadrature or degree-of-freedom is lost.

For an optical amplifier with large $n$ it holds $G$ ≥ 2 whereas for an electrical amplifier it holds $F_{pnf}$ ≥ 1.

Moreover, today's long-haul optical fiber communication is dominated by coherent optical I&Q receivers but $F_{e}$ does not describe the SNR degradation observed in these.

Another optical noise figure $F_{pnf}$ for amplified spontaneous emission has been defined. But the noise factor $F_{ase}$ is not the SNR degradation factor in any optical receiver.

All the above conflicts are resolved by the optical in-phase and quadrature noise factor and figure $F_{ase}$. It can be measured using a coherent optical I&Q receiver. In these, power of the output signal is proportional to the square of an optical field amplitude because they are linear in amplitude. They pass both quadratures. For an optical amplifier it holds $F_{o,IQ}$ = $F_{o,IQ}$ ≥ 1. Quantity $n_{sp}(1-1/G)+1/G$ is the input-referred number of added noise photons per mode.

$n_{sp}(1-1/G)$ and $F_{o,IQ}$ can easily be converted into each other. For large $F_{pnf}$ it holds $G$ = $F_{o,IQ}$ or, when expressed in dB, $F_{pnf}/2$ is 3 dB less than $F_{o,IQ}$. The ideal $F_{pnf}$ in dB equals 0 dB. This describes the known fact that the sensitivity of an ideal optical I&Q receiver is not improved by an ideal optical preamplifier.

title: Noise figure


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Noise level

The noise level is the level of noise. Specifically, it may refer to:
 * Noise (electronics)
 * Ambient noise level
 * Environmental noise

title: Noise level


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Noise power

In telecommunication, the term noise power has the following meanings:
 * 1) The measured total noise in a given bandwidth at the input or output of a device when the signal is not present; the integral of noise spectral density over the bandwidth
 * 2) The power generated by a random electromagnetic process.
 * 3) Interfering and unwanted power in an electrical device or system.
 * 4) In the acceptance testing of radio transmitters, the mean power supplied to the antenna transmission line by a radio transmitter when loaded with noise having a Gaussian amplitude-vs.-frequency distribution.

Noise power can be calculated by multiplying the noise spectral density with the signal bandwidth
 * $$N_\text{p} = k_\text{B}TB,$$

where
 * k$B$ = Boltzmann constant ≈
 * T = absolute temperature of the device
 * B = bandwidth

title: Noise power


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Noise temperature

In electronics, noise temperature is one way of expressing the level of available noise power introduced by a component or source. The power spectral density of the noise is expressed in terms of the temperature (in kelvins) that would produce that level of Johnson–Nyquist noise, thus:

 * $$\frac{P_\text{N}}{B} = k_\text{B} T  $$

where:

 * $$ P_\text{N}$$ is the noise power (in W, watts)
 * $$ B$$ is the total bandwidth (Hz, hertz) over which that noise power is measured
 * $$ k_\text{B}$$ is the Boltzmann constant ($1.381 J/K$, joules per kelvin)
 * $$ T$$ is the noise temperature (K, kelvin)

Thus the noise temperature is proportional to the power spectral density of the noise, $$P_\text{N}/ B$$. That is the power that would be absorbed from the component or source by a matched load. Noise temperature is generally a function of frequency, unlike that of an ideal resistor which is simply equal to the actual temperature of the resistor at all frequencies.

Noise voltage and current
A noisy component may be modelled as a noiseless component in series with a noisy voltage source producing a voltage of $v_{n}$, or as a noiseless component in parallel with a noisy current source producing a current of  $i_{n}$. This equivalent voltage or current corresponds to the above power spectral density $$\frac{P} {B}$$, and would have a mean squared amplitude over a bandwidth $B$ of:

 * $$\begin{align}

\frac{\bar{v}_\text{n}^2}{B} &= 4 k_\text{B} R T \\ \\ \frac{\bar{i}_\text{n}^2}{B} &= 4 k_\text{B} G T \end{align}$$

where $R$ is the resistive part of the component's impedance or $G$ is the conductance (real part) of the component's admittance. Speaking of noise temperature therefore offers a fair comparison between components having different impedances rather than specifying the noise voltage and qualifying that number by mentioning the component's resistance. It is also more accessible than speaking of the noise's power spectral density (in watts per hertz) since it is expressed as an ordinary temperature which can be compared to the noise level of an ideal resistor at room temperature (290 K).

Note that one can only speak of the noise temperature of a component or source whose impedance has a substantial (and measurable) resistive component. Thus it does not make sense to talk about the noise temperature of a capacitor or of a voltage source. The noise temperature of an amplifier refers to the noise that would be added at the amplifier's input (relative to the input impedance of the amplifier) in order to account for the added noise observed following amplification.

System noise temperature
An RF receiver system is typically made up of an antenna and a receiver, and the transmission line(s) that connect the two together. Each of these is a source of additive noise. The additive noise in a receiving system can be of thermal origin (thermal noise) or can be from other external or internal noise-generating processes. The contributions of all noise sources are typically lumped together and regarded as a level of thermal noise. The noise power spectral density generated by any source ($$ P / B$$) can be described by assigning to the noise a temperature $$T$$ as defined above:

 * $$T = \frac{P}{B} \cdot \frac{1}{k_\text{B}}$$

In an RF receiver, the overall system noise temperature $$T_S$$ equals the sum of the effective noise temperature of the receiver and transmission lines and that of the antenna.

 * $$T_{S} = T_{A} + T_{E}$$

The antenna noise temperature $$T_{A}$$ gives the noise power seen at the output of the antenna. The composite noise temperature of the receiver and transmission line losses $$T_{E}$$ represents the noise contribution of the rest of the receiver system. It is calculated as the effective noise that would be present at the antenna input terminals if the receiver system were perfect and created no noise. In other words, it is a cascaded system of amplifiers and losses where the internal noise temperatures are referred to the antenna input terminals. Thus, the summation of these two noise temperatures represents the noise input to a "perfect" receiver system.

Noise factor and noise figure
One use of noise temperature is in the definition of a system's noise factor or noise figure. The noise factor specifies the increase in noise power (referred to the input of an amplifier) due to a component or system when its input noise temperature is $$ T_{0}$$.

 * $$F = \frac{T_0 + T_\text{E}}{T_0}$$

$$T_0$$ is customarily taken to be room temperature, 290 K.

The noise factor (a linear term) is more often expressed as the noise figure (in decibels) using the conversion:
 * $$NF = 10 \log_{10} (F)$$

The noise figure can also be seen as the decrease in signal-to-noise ratio (SNR) caused by passing a signal through a system if the original signal had a noise temperature of 290 K. This is a common way of expressing the noise contributed by a radio frequency amplifier regardless of the amplifier's gain. For instance, assume an amplifier has a noise temperature 870 K and thus a noise figure of 6 dB. If that amplifier is used to amplify a source having a noise temperature of about room temperature (290 K), as many sources do, then the insertion of that amplifier would reduce the SNR of a signal by 6 dB. This simple relationship is frequently applicable where the source's noise is of thermal origin since a passive transducer will often have a noise temperature similar to 290 K.

However, in many cases the input source's noise temperature is much higher, such as an antenna at lower frequencies where atmospheric noise dominates. Then there will be little degradation of the SNR. On the other hand, a good satellite dish looking through the atmosphere into space (so that it sees a much lower noise temperature) would have the SNR of a signal degraded by more than 6 dB. In those cases a reference to the amplifier's noise temperature itself, rather than the noise figure defined according to room temperature, is more appropriate.

Effective noise temperature
The noise temperature of an amplifier is commonly measured using the Y-factor method. If there are multiple amplifiers in cascade, the noise temperature of the cascade can be calculated using the Friis equation:

 * $$T_\text{E} = T_1 + \frac{T_2}{G_1} + \frac{T_3}{G_1 G_2} + \cdots$$

where
 * $$ T_\text{E}$$ = resulting noise temperature referred to the input
 * $$ T_1$$ = noise temperature of the first component in the cascade
 * $$ T_2$$ = noise temperature of the second component in the cascade
 * $$ T_3$$ = noise temperature of the third component in the cascade
 * $$ G_1$$ = power gain of the first component in the cascade
 * $$ G_2$$ = power gain of the second component in the cascade

Therefore, the amplifier chain can be modelled as a black box having a gain of $$G_1 \cdot G_2 \cdot G_3 \cdots$$ and a noise figure given by $$NF = 10 \log_{10} (1 + T_\text{E}/290)$$. In the usual case where the gains of the amplifier's stages are much greater than one, then it can be seen that the noise temperatures of the earlier stages have a much greater influence on the resulting noise temperature than those later in the chain. One can appreciate that the noise introduced by the first stage, for instance, is amplified by all of the stages whereas the noise introduced by later stages undergoes lesser amplification. Another way of looking at it is that the signal applied to a later stage already has a high noise level, due to amplification of noise by the previous stages, so that the noise contribution of that stage to that already amplified signal is of less significance.

This explains why the quality of a preamplifier or RF amplifier is of particular importance in an amplifier chain. In most cases only the noise figure of the first stage need be considered. However one must check that the noise figure of the second stage is not so high (or that the gain of the first stage is so low) that there is SNR degradation due to the second stage anyway. That will be a concern if the noise figure of the first stage plus that stage's gain (in decibels) is not much greater than the noise figure of the second stage.

One corollary of the Friis equation is that an attenuator prior to the first amplifier will degrade the noise figure due to the amplifier. For instance, if stage 1 represents a 6 dB attenuator so that $$G_1 = \frac{1}{4}$$, then $$T_\text{E} = T_1 + 4 T_2 + \cdots$$. Effectively the noise temperature of the amplifier $$T_2$$ has been quadrupled, in addition to the (smaller) contribution due to the attenuator itself  $$T_1$$ (usually room temperature if the attenuator is composed of resistors). An antenna with poor efficiency is an example of this principle, where $$G_1$$ would represent the antenna's efficiency.

title: Noise temperature


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Noise weighting

A noise weighting is a specific amplitude-vs.-frequency characteristic that is designed to allow subjectively valid measurement of noise. It emphasises the parts of the spectrum that are most important.

Usually, noise means audible noise, in audio systems, broadcast systems or telephone circuits. In this case the weighting is sometimes referred to as Psophometric weighting, though this term is best avoided because, although strictly a general term, the word Psophometric is sometimes assumed to refer to a particular weighting used in telecommunications.

A major use of noise weighting is in the measurement of residual noise in audio equipment, usually present as hiss or hum in quiet moments of programme material. The purpose of weighting here is to emphasise the parts of the audible spectrum that our ears perceive most readily, and attenuate the parts that contribute less to our perception of loudness, in order to get a measured figure that correlates well with subjective effect.

The ITU-R 468 noise weighting was devised specifically for this purpose, and is widely used in broadcasting, especially in the UK and Europe. A-weighting is also used, especially in the United States, though this is only really valid for the measurement of tones, not noise, and is widely incorporated into sound level meters.

In telecommunication, noise weightings are used by agencies concerned with public telephone service, and various standard curves are based on the characteristics of specific commercial telephone instruments, representing successive stages of technological development. The coding of commercial apparatus appears in the nomenclature of certain weightings. The same weighting nomenclature and units are used in military versions of commercial noise measuring sets.

Telecommunication measurements are made in lines terminated either by the measuring set or an instrument of the relevant class.

title: Noise weighting


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Non-return-to-zero

In telecommunication, a non-return-to-zero (NRZ) line code is a binary code in which ones are represented by one significant condition, usually a positive voltage, while zeros are represented by some other significant condition, usually a negative voltage, with no other neutral or rest condition.

For a given data signaling rate, i.e., bit rate, the NRZ code requires only half the baseband bandwidth required by the Manchester code (the passband bandwidth is the same). The pulses in NRZ have more energy than a return-to-zero (RZ) code, which also has an additional rest state beside the conditions for ones and zeros.

When used to represent data in an asynchronous communication scheme, the absence of a neutral state requires other mechanisms for bit synchronization when a separate clock signal is not available. Since NRZ is not inherently a self-clocking signal, some additional synchronization technique must be used for avoiding bit slips; examples of such techniques are a run-length-limited constraint and a parallel synchronization signal.

Variants
NRZ can refer to any of the following serializer line codes:

The NRZ code also can be classified as a polar or non-polar, where polar refers to a mapping to voltages of +V and −V, and non-polar refers to a voltage mapping of +V and 0, for the corresponding binary values of 0 and 1.

Unipolar non-return-to-zero level

"One" is represented by a DC bias on the transmission line (conventionally positive), while "zero" is represented by the absence of bias – the line at 0 volts or grounded. For this reason it is also known as "on-off keying". In clock language, a "one" transitions to or remains at a biased level on the trailing clock edge of the previous bit, while "zero" transitions to or remains at no bias on the trailing clock edge of the previous bit. Among the disadvantages of unipolar NRZ is that it allows for long series without change, which makes synchronization difficult, although this is not unique to the unipolar case. One solution is to not send bytes without transitions. More critically, and unique to unipolar NRZ, are issues related to the presence of a transmitted DC level – the power spectrum of the transmitted signal does not approach zero at zero frequency. This leads to two significant problems: first, the transmitted DC power leads to higher power losses than other encodings, and second, the presence of a DC signal component requires that the transmission line be DC-coupled.

Bipolar non-return-to-zero level
"One" is represented by one physical level (usually a positive voltage), while "zero" is represented by another level (usually a negative voltage). In clock language, in bipolar NRZ-level the voltage "swings" from positive to negative on the trailing edge of the previous bit clock cycle.

An example of this is RS-232, where "one" is −12 V to −5 V and "zero" is +5 V to +12 V.

Non-return-to-zero space
"One" is represented by no change in physical level, while "zero" is represented by a change in physical level. In clock language, the level transitions on the trailing clock edge of the previous bit to represent a "zero".

This "change-on-zero" is used by High-Level Data Link Control and USB. They both avoid long periods of no transitions (even when the data contains long sequences of 1 bits) by using zero-bit insertion. HDLC transmitters insert a 0 bit after 5 contiguous 1 bits (except when transmitting the frame delimiter "01111110"). USB transmitters insert a 0 bit after 6 consecutive 1 bits. The receiver at the far end uses every transition — both from 0 bits in the data and these extra non-data 0 bits — to maintain clock synchronization. The receiver otherwise ignores these non-data 0 bits.

Non-return-to-zero inverted
Non-return-to-zero, inverted (NRZI, also known as non-return to zero IBM, inhibit code, or IBM code ) was devised by Bryon E. Phelps (IBM) in 1956. It is a method of mapping a binary signal to a physical signal for transmission over some transmission medium. The two-level NRZI signal distinguishes data bits by the presence or absence of a transition at a clock boundary. The NRZI encoded signal can be decoded unambiguously after passing through a data path that doesn’t preserve polarity.

Which bit value corresponds to a transition varies in practice, NRZI applies equally to both. Magnetic storage generally uses the NRZ-M, non-return-to-zero mark convention: a logical 1 is encoded as a transition, and a logical 0 is encoded as no transition. The HDLC and Universal Serial Bus protocols use the opposite NRZ-S, non-return-to-zero space convention: a logical 0 is a transition, and a logical 1 is no transition. Neither NRZI encoding guarantees that the encoded bitstream has transitions.

An asynchronous receiver uses an independent bit clock that is phase synchronized by detecting bit transitions. When an asynchronous receiver decodes a block of bits without a transition longer than the period of the difference between the frequency of the transmitting and receiving bit clocks, the decoder’s bit clock is either 1 bit earlier than the encoder resulting in a duplicated bit being inserted in the decoded data stream, or the decoder’s bit clock is 1 bit later than the encoder resulting in a duplicated bit being removed from the decoded data stream. Both are referred to as “bit slip” denoting that the phase of the bit clock has slipped a bit period.

Forcing transitions at intervals shorter than the bit clock difference period allows an asynchronous receiver to be used for NRZI bit streams. Additional transitions necessarily consume some of the data channel’s rate capacity. Consuming no more of the channel capacity than necessary to maintain bit clock synchronization without increasing costs related to complexity is a problem with many possible solutions.

Run-length limited (RLL) encodings have been used for magnetic disk and tape storage devices using fixed-rate RLL codes that increase the channel data rate by a known fraction of the information data rate. HDLC and USB use bit stuffing: inserting an additional 0 bit before NRZ-S encoding to force a transition in the encoded data sequence after 5 (HLDC) or 6 (USB) consecutive 1 bits. Bit stuffing consumes channel capacity only when necessary but results in a variable information data rate.

Synchronized non-return-to-zero
Synchronized NRZI (SNRZI) and group-coded recording (GCR) are modified forms of NRZI. In SNRZI-M each 8-bit group is extended to 9 bits by a 1 in order to insert a transition for synchronisation.

Comparison with return-to-zero
Return-to-zero describes a line code used in telecommunications in which the signal drops (returns) to zero between each pulse. This takes place even if a number of consecutive 0s or 1s occur in the signal. The signal is self-clocking. This means that a separate clock does not need to be sent alongside the signal, but suffers from using twice the bandwidth to achieve the same data-rate as compared to non-return-to-zero format.

The zero between each bit is a neutral or rest condition, such as a zero amplitude in pulse-amplitude modulation (PAM), zero phase shift in phase-shift keying (PSK), or mid-frequency in frequency-shift keying (FSK). That zero condition is typically halfway between the significant condition representing a 1 bit and the other significant condition representing a 0 bit.

Although return-to-zero contains a provision for synchronization, it still may have a DC component resulting in baseline wander during long strings of 0 or 1 bits, just like the line code non-return-to-zero.

title: Non-return-to-zero


text:
Normalized frequency

Normalized frequency can refer to:
 * Normalized frequency (digital signal processing)
 * Normalized frequency (fiber optics), also known as V number

title: Normalized frequency


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NS/EP telecommunications

NS/EP telecommunications is an abbreviation for National Security or Emergency Preparedness telecommunications of the United States. Telecommunications services that are used to maintain a state of readiness or to respond to and manage any event or crisis (local, national, or international) that causes or could cause injury or harm to the population, damage to or loss of property, or degrade or threaten the national security or emergency preparedness posture of the United States.

NS/EP telecommunications are managed and controlled by the National Communications System using Telecommunications Service Priority through both the Government Emergency Telecommunications Service and Wireless Priority Service.

title: NS/EP telecommunications


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N-entity

In telecommunication, a n-entity is an active element in the n-th layer of the Open Systems Interconnection--Reference Model (OSI-RM) that (a) interacts directly with elements, i.e., entities, of the layer immediately above or below the n-th layer, (b) is defined by a unique set of rules, i.e., syntax, and information formats, including data and control formats, and (c) performs a defined set of functions.

The n refers to any one of the 7 layers of the OSI-RM.

In an existing layered open system, the n may refer to any given layer in the system.

Layers are conventionally numbered from the lowest, i.e., the physical layer, to the highest, so that the (n + 1)-th layer is above the n-th layer and the (n − 1)-th layer is below.

title: N-entity


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Numerical aperture

In optics, the numerical aperture (NA) of an optical system is a dimensionless number that characterizes the range of angles over which the system can accept or emit light. By incorporating index of refraction in its definition, NA has the property that it is constant for a beam as it goes from one material to another, provided there is no refractive power at the interface. The exact definition of the term varies slightly between different areas of optics. Numerical aperture is commonly used in microscopy to describe the acceptance cone of an objective (and hence its light-gathering ability and resolution), and in fiber optics, in which it describes the range of angles within which light that is incident on the fiber will be transmitted along it.

General optics
In most areas of optics, and especially in microscopy, the numerical aperture of an optical system such as an objective lens is defined by

$$\mathrm{NA} = n \sin \theta,$$

where $θ1$ is the index of refraction of the medium in which the lens is working (1.00 for air, 1.33 for pure water, and typically 1.52 for immersion oil; see also list of refractive indices), and $θ2$ is the half-angle of the maximum cone of light that can enter or exit the lens. In general, this is the angle of the real marginal ray in the system. Because the index of refraction is included, the NA of a pencil of rays is an invariant as a pencil of rays passes from one material to another through a flat surface. This is easily shown by rearranging Snell's law to find that $NA = n1sin θ1 = n2sin θ2$ is constant across an interface.

In air, the angular aperture of the lens is approximately twice this value (within the paraxial approximation). The NA is generally measured with respect to a particular object or image point and will vary as that point is moved. In microscopy, NA generally refers to object-space numerical aperture unless otherwise noted.

In microscopy, NA is important because it indicates the resolving power of a lens. The size of the finest detail that can be resolved (the resolution) is proportional to $n$, where $θ$ is the wavelength of the light. A lens with a larger numerical aperture will be able to visualize finer details than a lens with a smaller numerical aperture. Assuming quality (diffraction-limited) optics, lenses with larger numerical apertures collect more light and will generally provide a brighter image, but will provide shallower depth of field.

Numerical aperture is used to define the "pit size" in optical disc formats.

Increasing the magnification and the numerical aperture of the objective reduces the working distance, i.e. the distance between front lens and specimen.

Numerical aperture versus f-number

Numerical aperture is not typically used in photography. Instead, the angular aperture of a lens (or an imaging mirror) is expressed by the f-number, written, where $P$ is the f-number given by the ratio of the focal length $N$ to the diameter of the entrance pupil $n sin θ$:

$$N = \frac{f}{D}.$$

This ratio is related to the image-space numerical aperture when the lens is focused at infinity. Based on the diagram at the right, the image-space numerical aperture of the lens is:

$$\text{NA}_\text{i} = n \sin \theta = n \sin \left[ \arctan \left( \frac{D}{2f} \right) \right] \approx n \frac{D}{2f},$$

thus $λ⁄2NA$, assuming normal use in air ($λ$).

The approximation holds when the numerical aperture is small, but it turns out that for well-corrected optical systems such as camera lenses, a more detailed analysis shows that $D$ is almost exactly equal to $N ≈ 1⁄2NA_{i}$ even at large numerical apertures. As Rudolf Kingslake explains, "It is a common error to suppose that the ratio [$n = 1$] is actually equal to $N$, and not $1/(2NA_{i})$ ... The tangent would, of course, be correct if the principal planes were really plane.  However, the complete theory of the Abbe sine condition shows that if a lens is corrected for coma and spherical aberration, as all good photographic objectives must be, the second principal plane becomes a portion of a sphere of radius $f$ centered about the focal point". In this sense, the traditional thin-lens definition and illustration of f-number is misleading, and defining it in terms of numerical aperture may be more meaningful.

Working (effective) f-number
The f-number describes the light-gathering ability of the lens in the case where the marginal rays on the object side are parallel to the axis of the lens. This case is commonly encountered in photography, where objects being photographed are often far from the camera. When the object is not distant from the lens, however, the image is no longer formed in the lens's focal plane, and the f-number no longer accurately describes the light-gathering ability of the lens or the image-side numerical aperture. In this case, the numerical aperture is related to what is sometimes called the "working f-number" or "effective f-number".

The working f-number is defined by modifying the relation above, taking into account the magnification from object to image:

$$\frac{1}{2 \text{NA}_\text{i}} = N_\text{w} = \left(1 - \frac{m}{P}\right) N, $$

where $D/2f$ is the working f-number, $tan θ$ is the lens's magnification for an object a particular distance away, $sin θ$ is the pupil magnification, and the NA is defined in terms of the angle of the marginal ray as before. The magnification here is typically negative, and the pupil magnification is most often assumed to be 1 — as Allen R. Greenleaf explains, "Illuminance varies inversely as the square of the distance between the exit pupil of the lens and the position of the plate or film. Because the position of the exit pupil usually is unknown to the user of a lens, the rear conjugate focal distance is used instead; the resultant theoretical error so introduced is insignificant with most types of photographic lenses."

In photography, the factor is sometimes written as $N_{w}$, where $m$ represents the absolute value of the magnification; in either case, the correction factor is 1 or greater. The two equalities in the equation above are each taken by various authors as the definition of working f-number, as the cited sources illustrate. They are not necessarily both exact, but are often treated as if they are.

Conversely, the object-side numerical aperture is related to the f-number by way of the magnification (tending to zero for a distant object):

$$\frac{1}{2 \text{NA}_\text{o}} = \frac{m - P}{mP} N. $$

Laser physics
In laser physics, numerical aperture is defined slightly differently. Laser beams spread out as they propagate, but slowly. Far away from the narrowest part of the beam, the spread is roughly linear with distance—the laser beam forms a cone of light in the "far field". The relation used to define the NA of the laser beam is the same as that used for an optical system,

$$\text{NA} = n \sin \theta,$$

but $P$ is defined differently. Laser beams typically do not have sharp edges like the cone of light that passes through the aperture of a lens does. Instead, the irradiance falls off gradually away from the center of the beam. It is very common for the beam to have a Gaussian profile. Laser physicists typically choose to make $1 + m$ the divergence of the beam: the far-field angle between the beam axis and the distance from the axis at which the irradiance drops to $m$ times the on-axis irradiance. The NA of a Gaussian laser beam is then related to its minimum spot size ("beam waist") by

$$\text{NA} \simeq \frac{\lambda_0}{\pi w_0},$$

where $θ$ is the vacuum wavelength of the light, and $θ$ is the diameter of the beam at its narrowest spot, measured between the $e^{−2}$ irradiance points ("Full width at $λ_{0}$ maximum of the intensity"). This means that a laser beam that is focused to a small spot will spread out quickly as it moves away from the focus, while a large-diameter laser beam can stay roughly the same size over a very long distance. See also: Gaussian beam width.

Fiber optics

A multi-mode optical fiber will only propagate light that enters the fiber within a certain range of angles, known as the acceptance cone of the fiber. The half-angle of this cone is called the acceptance angle, $2w_{0}$. For step-index multimode fiber in a given medium, the acceptance angle is determined only by the indices of refraction of the core, the cladding, and the medium: $$n \sin \theta_\max = \sqrt{n_\text{core}^2 - n_\text{clad}^2},$$ where $e^{−2}$ is the refractive index of the medium around the fiber, $e^{−2}$ is the refractive index of the fiber core, and $n_{1}$ is the refractive index of the cladding. While the core will accept light at higher angles, those rays will not totally reflect off the core–cladding interface, and so will not be transmitted to the other end of the fiber. The derivation of this formula is given below.

When a light ray is incident from a medium of refractive index $f$ to the core of index $n_{2}$ at the maximum acceptance angle, Snell's law at the medium–core interface gives $$n\sin\theta_\max = n_\text{core}\sin\theta_r.\ $$

From the geometry of the above figure we have: $$\sin\theta_{r} = \sin\left({90^\circ} - \theta_{c}\right) = \cos\theta_{c}$$

where $$ \theta_{c} = \arcsin \frac{n_\text{clad}}{n_\text{core}}$$

is the critical angle for total internal reflection.

Substituting $θ_{max}$ for $n$ in Snell's law we get: $$\frac{n}{n_\text{core}}\sin\theta_\max = \cos\theta_{c}.$$

By squaring both sides $$\frac{n^{2}}{n_\text{core}^{2}}\sin^{2}\theta_\max = \cos^{2}\theta_{c} = 1 - \sin^{2}\theta_{c} = 1 - \frac{n_\text{clad}^{2}}{n_\text{core}^{2}}.$$

Solving, we find the formula stated above:

$$n \sin \theta_\max = \sqrt{n_\text{core}^2 - n_\text{clad}^2},$$

This has the same form as the numerical aperture in other optical systems, so it has become common to define the NA of any type of fiber to be $$\mathrm{NA} = \sqrt{n_\text{core}^2 - n_\text{clad}^2},$$

where $n_{core}$ is the refractive index along the central axis of the fiber. Note that when this definition is used, the connection between the numerical aperture and the acceptance angle of the fiber becomes only an approximation. In particular, manufacturers often quote "NA" for single-mode fiber based on this formula, even though the acceptance angle for single-mode fiber is quite different and cannot be determined from the indices of refraction alone.

The number of bound modes, the mode volume, is related to the normalized frequency and thus to the numerical aperture.

In multimode fibers, the term equilibrium numerical aperture is sometimes used. This refers to the numerical aperture with respect to the extreme exit angle of a ray emerging from a fiber in which equilibrium mode distribution has been established.

title: Numerical aperture


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Nyquist rate

In signal processing, the Nyquist rate, named after Harry Nyquist, is a value equal to twice the highest frequency (bandwidth) of a given function or signal. It has units of samples per unit time, conventionally expressed as samples per second, or hertz (Hz). When the signal is sampled at a higher sample rate (see ), the resulting discrete-time sequence is said to be free of the distortion known as aliasing. Conversely, for a given sample rate the corresponding Nyquist frequency is one-half the sample rate. Note that the Nyquist rate is a property of a continuous-time signal, whereas Nyquist frequency is a property of a discrete-time system.

The term Nyquist rate is also used in a different context with units of symbols per second, which is actually the field in which Harry Nyquist was working. In that context it is an upper bound for the symbol rate across a bandwidth-limited baseband channel such as a telegraph line or passband channel such as a limited radio frequency band or a frequency division multiplex channel.

Relative to sampling
When a continuous function, $$x(t),$$ is sampled at a constant rate, $$f_s$$ samples/second, there is always an unlimited number of other continuous functions that fit the same set of samples. But only one of them is bandlimited to $$\tfrac{1}{2}f_s$$ cycles/second (hertz), which means that its Fourier transform, $$X(f),$$ is $$0$$ for all $$|f| \ge \tfrac{1}{2}f_s.$$ The mathematical algorithms that are typically used to recreate a continuous function from samples create arbitrarily good approximations to this theoretical, but infinitely long, function. It follows that if the original function, $$x(t),$$ is bandlimited to $$\tfrac{1}{2}f_s,$$ which is called the Nyquist criterion, then it is the one unique function the interpolation algorithms are approximating. In terms of a function's own bandwidth $$(B), $$ as depicted here, the Nyquist criterion is often stated as $$f_s > 2B.$$ And $$2B$$ is called the Nyquist rate for functions with bandwidth $$B.$$  When the Nyquist criterion is not met $($say, $B > \tfrac{1}{2}f_s),$ a condition called aliasing occurs, which results in some inevitable differences between $$x(t)$$ and a reconstructed function that has less bandwidth. In most cases, the differences are viewed as distortion.

Intentional aliasing
Figure 3 depicts a type of function called baseband or lowpass, because its positive-frequency range of significant energy is [0, B). When instead, the frequency range is (A, A+B), for some A > B, it is called bandpass, and a common desire (for various reasons) is to convert it to baseband.  One way to do that is frequency-mixing (heterodyne) the bandpass function down to the frequency range (0, B).  One of the possible reasons is to reduce the Nyquist rate for more efficient storage.  And it turns out that one can directly achieve the same result by sampling the bandpass function at a sub-Nyquist sample-rate that is the smallest integer-sub-multiple of frequency A that meets the baseband Nyquist criterion:  fs > 2B.  For a more general discussion, see bandpass sampling.

Relative to signaling
Long before Harry Nyquist had his name associated with sampling, the term Nyquist rate was used differently, with a meaning closer to what Nyquist actually studied. Quoting Harold S. Black's 1953 book Modulation Theory, in the section Nyquist Interval of the opening chapter Historical Background:

 * "If the essential frequency range is limited to B cycles per second, 2B was given by Nyquist as the maximum number of code elements per second that could be unambiguously resolved, assuming the peak interference is less than half a quantum step. This rate is generally referred to as signaling at the Nyquist rate and 1/(2B) has been termed a Nyquist interval." (bold added for emphasis; italics from the original)

According to the OED, Black's statement regarding 2B may be the origin of the term Nyquist rate.

Nyquist's famous 1928 paper was a study on how many pulses (code elements) could be transmitted per second, and recovered, through a channel of limited bandwidth. Signaling at the Nyquist rate meant putting as many code pulses through a telegraph channel as its bandwidth would allow. Shannon used Nyquist's approach when he proved the sampling theorem in 1948, but Nyquist did not work on sampling per se.

Black's later chapter on "The Sampling Principle" does give Nyquist some of the credit for some relevant math:

 * "Nyquist (1928) pointed out that, if the function is substantially limited to the time interval T, 2BT values are sufficient to specify the function, basing his conclusions on a Fourier series representation of the function over the time interval T."

title: Nyquist rate


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Off-axis optical system

An off-axis optical system is an optical system in which the optical axis of the aperture is not coincident with the mechanical center of the aperture. The principal applications of off-axis optical systems are to avoid obstruction of the primary aperture by secondary optical elements, instrument packages, or sensors, and to provide ready access to instrument packages or sensors at the focus. The engineering tradeoff of an off-axis optical system is an increase in image aberrations.

There are various theoretical models for aberration in off-axis optical systems. This involves various techniques including different types of equations for ray-tracing, and a goal can be optimizing the design.

An example of an off-axis optical system is a three mirror design as optics for a hyperspectral imager.

title: Off-axis optical system


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On- and off-hook

In telephony, on-hook and off-hook are two states of a communication circuit. On subscriber telephones the states are produced by placing the handset onto or off the hookswitch. Placing the circuit into the off-hook state is also called seizing the line. Off-hook originally referred to the condition that prevailed when telephones had a separate earpiece (receiver), which hung from its switchhook until the user initiated a telephone call by removing it. When off hook the weight of the receiver no longer depresses the spring-loaded switchhook, thereby connecting the instrument to the telephone line.

Off-hook
The term off-hook has the following meanings:
 * The condition that exists when a telephone or other user instrument is in use, i.e., during dialing or communicating.
 * A general description of one of two possible signaling states at an interface between telecommunications systems, such as tone or no tone and ground connection versus battery connection. Note that if off-hook pertains to one state, on-hook pertains to the other.
 * The active state (i.e., a closed loop (short circuit between the wires) of a subscriber line or PBX user loop)
 * An operating state of a communications link in which data transmission is enabled either for (a) voice or data communications or (b) network signaling.

On an ordinary two-wire telephone line, off-hook status is communicated to the telephone exchange by a resistance short across the pair. When an off-hook condition persists without dialing, for example because the handset has fallen off or the cable has been flooded, it is treated as a permanent loop or permanent signal.

The act of going off-hook is also referred to as seizing the line or channel.

On-hook
The term on-hook has the following meanings:
 * The condition that exists when a telephone or other user instrument is not in use, i.e., when idle waiting for a call. Note: on-hook originally referred to the storage of an idle telephone receiver, i.e., separate earpiece, on a switchhook. The weight of the receiver depresses the spring-loaded switchhook thereby disconnecting the idle instrument (except its bell) from the telephone line.
 * One of two possible signaling states, such as tone or no tone, or ground connection versus battery connection. Note: if on-hook pertains to one state, off-hook pertains to the other.
 * The idle state, i.e., an open loop of a subscriber line or PBX user loop.
 * An operating state of a telecommunication circuit in which transmission is disabled and a high impedance, or "open circuit", is presented to the link by the end instrument(s). Note: during the on-hook condition, the link is responsive to ringing signals.

The act of going on-hook is also referred to as releasing the line or channel, and may initiate the process of clearing.

title: On- and off-hook


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Online and offline

In computer technology and telecommunications, online indicates a state of connectivity, and offline indicates a disconnected state. In modern terminology, this usually refers to an Internet connection, but (especially when expressed as "on line" or "on the line") could refer to any piece of equipment or functional unit that is connected to a larger system. Being online means that the equipment or subsystem is connected, or that it is ready for use.

"Online" has come to describe activities performed on and data available on the Internet, for example: "online identity", "online predator", "online gambling", "online game", "online shopping", "online banking", and "online learning". A Similar meaning is also given by the prefixes "cyber" and "e", as in words "cyberspace", "cybercrime", "email", and "e-commerce". In contrast, "offline" can refer to either computing activities performed while disconnected from the Internet, or alternatives to Internet activities (such as shopping in brick-and-mortar stores). The term "offline" is sometimes used interchangeably with the acronym "IRL", meaning "in real life".

History
During the 19th century, the term on line was commonly used in both the railroad and telegraph industries. For railroads, a signal box would send messages down the line (track), via a telegraph line (cable), indicating the track's status: Train on line or Line clear. Telegraph linemen would refer to sending current through a line as direct on line or battery on line; or they may refer to a problem with the circuit as being on line, as opposed to the power source or end-point equipment.

Since at least 1950, in computing, the terms on-line and off-line have been used to refer to whether machines, including computers and peripheral devices, are connected or not. Here is an excerpt from the 1950 book High-Speed Computing Devices:

 * The use of automatic computing equipment for large-scale reduction of data will be strikingly successful only if means are provided for the automatic transcription of these data to a form suitable for automatic entry into the machine. For some applications, of which the most prominent are those in which the reduced data are used to control the process being measured, the input must be developed for on-line operation. In on-line operation the input is communicated directly and without delay to the data-reduction device. For other applications, off-line operation, involving automatic transcription of data in a form suitable for later introduction to the machine, may be tolerated. These requirements may be compared with teleprinter operating requirements. For example, some teletype machines operate on line. Their operators are in instantaneous communication. Other teletype machines are operated off line, through the intervention of punched paper tape. The message is preserved by means of holes punched in the tape and is transmitted later by feeding the tape to another machine.

Offline e-mail
One example of a common use of these concepts with email is a mail user agent (MUA) that can be instructed to be in either online or offline states. One such MUA is Microsoft Outlook. When online it will attempt to connect to mail servers (to check for new mail at regular intervals, for example), and when offline it will not attempt to make any such connection. The online or offline state of the MUA does not necessarily reflect the connection status between the computer on which it is running and the Internet i.e. the computer itself may be online—connected to the Internet via a cable modem or other means—while Outlook is kept offline by the user, so that it makes no attempt to send or to receive messages. Similarly, a computer may be configured to employ a dial-up connection on demand (as when an application such as Outlook attempts to make a connection to a server), but the user may not wish for Outlook to trigger that call whenever it is configured to check for mail.

Offline media playing
Another example of the use of these concepts is digital audio technology. A tape recorder, digital audio editor, or other device that is online is one whose clock is under the control of the clock of a synchronization master device. When the sync master commences playback, the online device automatically synchronizes itself to the master and commences playing from the same point in the recording. A device that is offline uses no external clock reference and relies upon its own internal clock. When many devices are connected to a sync master it is often convenient, if one wants to hear just the output of one single device, to take it offline because, if the device is played back online, all synchronized devices have to locate the playback point and wait for each other device to be in synchronization. (For related discussion, see MIDI timecode, Word clock, and recording system synchronization.)

Offline browsing
A third example of a common use of these concepts is a web browser that can be instructed to be in either online or offline states. The browser attempts to fetch pages from servers while only in the online state. In the offline state, or "offline mode", users can perform offline browsing, where pages can be browsed using local copies of those pages that have previously been downloaded while in the online state. This can be useful when the computer is offline and connection to the Internet is impossible or undesirable. The pages are downloaded either implicitly into the web browser's own cache as a result of prior online browsing by the user or explicitly by a browser configured to keep local copies of certain web pages, which are updated when the browser is in the online state, either by checking that the local copies are up-to-date at regular intervals or by checking that the local copies are up-to-date whenever the browser is switched to the online. One such web browser is Internet Explorer. When pages are added to the Favourites list, they can be marked to be "available for offline browsing". Internet Explorer will download local copies of both the marked page and, optionally, all of the pages that it links to. In Internet Explorer version 6, the level of direct and indirect links, the maximum amount of local disc space allowed to be consumed, and the schedule on which local copies are checked to see whether they are up-to-date, are configurable for each individual Favourites entry.

For communities that lack adequate Internet connectivity—such as developing countries, rural areas, and prisons—offline information stores such as WiderNet's eGranary Digital Library (a collection of approximately thirty million educational resources from more than two thousand web sites and hundreds of CD-ROMs) provide offline access to information. More recently, the Internet Archive announced an offline server project intended to provide access to material on inexpensive servers that can be updated using USB sticks and SD cards.

Offline storage
Likewise, offline storage is computer data storage that has no connection to the other systems until a connection is deliberately made. Additionally, an otherwise online system that is powered down may be considered offline.

Offline messages
With the growing communication tools and media, the words offline and online are used very frequently. If a person is active over a messaging tool and is able to accept the messages it is termed as online message and if the person is not available and the message is left to view when the person is back, it is termed as offline message. In the same context, the person's availability is termed as online and non-availability is termed as offline.

File systems
In the context of file systems, "online" and "offline" are synonymous with "mounted" and "not mounted". For example, in file systems' resizing capabilities, "online grow" and "online shrink" respectively mean the ability to increase or decrease the space allocated to that file system without needing to unmount it.

Generalisations
Online and offline distinctions have been generalised from computing and telecommunication into the field of human interpersonal relationships. The distinction between what is considered online and what is considered offline has become a subject of study in the field of sociology.

The distinction between online and offline is conventionally seen as the distinction between computer-mediated communication and face-to-face communication (e.g., face time), respectively. Online is virtuality or cyberspace, and offline is reality (i.e., real life or "meatspace"). Slater states that this distinction is "obviously far too simple". To support his argument that the distinctions in relationships are more complex than a simple dichotomy of online versus offline, he observes that some people draw no distinction between an online relationship, such as indulging in cybersex, and an offline relationship, such as being pen pals. He argues that even the telephone can be regarded as an online experience in some circumstances, and that the blurring of the distinctions between the uses of various technologies (such as PDA versus mobile phone, internet television versus internet, and telephone versus Voice over Internet Protocol) has made it "impossible to use the term online meaningfully in the sense that was employed by the first generation of Internet research".

Slater asserts that there are legal and regulatory pressures to reduce the distinction between online and offline, with a "general tendency to assimilate online to offline and erase the distinction," stressing, however, that this does not mean that online relationships are being reduced to pre-existing offline relationships. He conjectures that greater legal status may be assigned to online relationships (pointing out that contractual relationships, such as business transactions, online are already seen as just as "real" as their offline counterparts), although he states it to be hard to imagine courts awarding palimony to people who have had a purely online sexual relationship. He also conjectures that an online/offline distinction may be seen by people as "rather quaint and not quite comprehensible" within 10 years.

This distinction between online and offline is sometimes inverted, with online concepts being used to define and to explain offline activities, rather than (as per the conventions of the desktop metaphor with its desktops, trash cans, folders, and so forth) the other way around. Several cartoons appearing in The New Yorker have satirized this. One includes Saint Peter asking for a username and a password before admitting a man into Heaven. Another illustrates "the offline store" where "All items are actual size!", shoppers may "Take it home as soon as you pay for it!", and "Merchandise may be handled prior to purchase!"

title: Online and offline


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One-way trunk

In telecommunication, a one-way trunk is a trunk between two switching centers, over which traffic may be originated from one preassigned location only.

The traffic may consist of two-way communications; the expression "one way" refers only to the origin of the demand for a connection. At the originating end, the one-way trunk is known as an "outgoing trunk"; at the other end, it is known as an "incoming trunk".

title: One-way trunk


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On-premises wiring

On-premises wiring (customer premises wiring) is customer-owned telecommunication transmission or distribution lines. The transmission lines may be metallic (copper) or optical fiber, and may be installed within or between buildings.

Premises wiring may consist of horizontal wiring, vertical wiring, and backbone cabling. It may extend from the point-of-entry to user work areas. Any type of telecommunications or data wiring is considered premises wiring, including telephone, computer/data, intercom, closed-circuit television.

Premises networks are wired worldwide, across every industry, in both small and large-scale applications. Any type or number of topologies may be used – star, bus, ring, etc. In 1989, the United States Federal Communications Commission (FCC) deregulated charges for maintaining at home inside wiring; the corresponding monthly charge was dropped January 1990.

Ownership
The ownership of on-premises wiring varies between jurisdictions: It depends on the location of the demarcation point. The location determines ownership and responsibility for maintenance and repair.

In the United States and Canada, most premises wiring is owned by the customer. There generally is a demarcation point "as close to the poles" as possible. For many installations, this is a network interface device mounted on the outside of the building. In some cases, it is a minimum-point-of-entry (MPOE) location inside the building.

In the United Kingdom, the demarcation point is the wall jack, and hence most of the on-premises wiring is the property of the telephone company.

title: On-premises wiring


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Open network architecture

In telecommunications, and in the context of Federal Communications Commission's (FCC) Computer Inquiry III, Open network architecture (ONA) is the overall design of a communication carrier's basic network facilities and services to permit all users of the basic network to interconnect to specific basic network functions and interfaces on an unbundled, equal-access basis.

The ONA concept consists of three integral components:

 * 1) Basic serving arrangements (BSAs)
 * 2) Basic service elements (BSEs)
 * 3) Complementary network services

title: Open network architecture


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Open systems architecture

Open systems architecture is a system design approach which aims to produce systems that are inherently interoperable and connectable without recourse to retrofit and redesign.

Concept
Systems design is a process of defining and engineering the architecture, methods, and interfaces necessary to accomplish a goal or fulfill a set of requirements. In open systems architecture, the design includes intentional provisions to make it possible to expand or modify the system at a later stage after initial operation. There is no one specific universal OSA, but it is essential the specific OSA applicable to a system is rigorously defined and documented. For example, in information technology and telecommunication, such design principles lead to open systems.

Telecommunications
In telecommunication, open systems architecture (OSA) is a standard that describes the layered hierarchical structure, configuration, or model of a communications or distributed data processing system. It enables system description, design, development, installation, operation, improvement, and maintenance to be performed at the abstraction layers in the hierarchical structure. Each layer provides a set of accessible functions that can be controlled and used by the functions in the layer above it. Each layer can be implemented without affecting the implementation of other layers. The alteration of system performance by the modification of one or more layers may be accomplished without altering the existing equipment, procedures, and protocols at the remaining layers.

Examples of independent alterations include the conversion from wire to optical fiber at a physical layer without affecting the data link layer or the network layer, except to provide more traffic capacity, and the altering of the operational protocols at the network level without altering the physical layer.

title: Open systems architecture


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Operation

Operation or Operations may refer to:

Arts, entertainment and media

 * Operation (game), a battery-operated board game that challenges dexterity
 * Operation (music), a term used in musical set theory
 * Operations (magazine), Multi-Man Publishing's house organ for articles and discussion about its wargaming products
 * The Operation (film), a 1973 British television film
 * The Operation (1990), a crime, drama, TV movie starring Joe Penny, Lisa Hartman, and Jason Beghe
 * The Operation M.D., formerly The Operation, a Canadian garage rock band
 * "Operation", a song by Relient K from The Creepy EP, 2001

Episodes

 * "The Operation", Sky Dancers episode 27 (1996)
 * "The Operation", The Golden Girls season 1, episode 18 (1986)
 * "The Operation", You're Only Young Twice (1997) series 2, episode 8 (1978)

Shows

 * The Operation (1992–1998), a reality television series from TLC

Business

 * Business operations, the harvesting of value from assets owned by a business
 * Manufacturing operations, operation of a facility
 * Operations management, an area of management concerned with designing and controlling the process of production

Military and law enforcement

 * Military operation, a military action (usually in a military campaign) using deployed forces
 * Black operation, or "Black op", an operation that may be outside of standard military protocol or against the law
 * Clandestine operation, an intelligence or military operation carried out so that the operation goes unnoticed
 * Combined operations, operations by forces of two or more allied nations
 * Covert operation, an operation which conceals the identity of the sponsor
 * Psychological operations, an operation consisting of psychological manipulations, tactics, and warfare
 * Special operations, military operations that are unconventional
 * Operations (J3), third level of Nation Level Command Structure
 * Operations (military staff), staff involved in planning operations
 * Sting operation, an operation designed to catch a person committing a crime, by means of deception

Science and technology

 * Inference, a step in reasoning
 * Information technology operations
 * Operation (mathematics), a calculation from zero or more input values (called operands) to an output value
 * Arity, number of arguments or operands that the function takes
 * Binary operation, calculation that combines two elements of the set to produce another element of the set
 * Graph operations, produce new graphs from initial ones
 * Modulo operation, operation finds the remainder after division of one number by another
 * Operations research, in British usage, application of advanced analytical methods to make better decisions
 * Unary operation, an operation with only one operand
 * Rail transport operations, the control of a rail system
 * Scientific operation
 * Surgical operation, or surgery, in medicine
 * Unit operation, a basic step in a chemical engineering process

Other uses

 * Anomalous operation, in parapsychology, a term describing a broad category of purported paranormal effects
 * Operation, a word which represents a grammatical relation (i.e., function) or instruction, rather than a term or name
 * Operation of law, a legal term that indicates that a right or liability has been created for a party

title: Operation


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Optical attenuator

An optical attenuator, or fiber optic attenuator, is a device used to reduce the power level of an optical signal, either in free space or in an optical fiber. The basic types of optical attenuators are fixed, step-wise variable, and continuously variable.

Applications
Optical attenuators are commonly used in fiber optic communications, either to test power level margins by temporarily adding a calibrated amount of signal loss, or installed permanently to properly match transmitter and receiver levels. Sharp bends stress optic fibers and can cause losses. If a received signal is too strong a temporary fix is to wrap the cable around a pencil until the desired level of attenuation is achieved. However, such arrangements are unreliable, since the stressed fiber tends to break over time. Generally, multimode systems do not need attenuators as the multimode sources, rarely have enough power output to saturate receivers. Instead, single-mode systems, especially the long-haul DWDM network links, often need to use fiber optic attenuators to adjust the optical power during the transmission.

Principles of operation
The power reduction is done by such means as absorption, reflection, diffusion, scattering, deflection, diffraction, and dispersion, etc. Optical attenuators usually work by absorbing the light, like sunglasses absorb extra light energy. They typically have a working wavelength range in which they absorb all light energy equally. They should not reflect the light or scatter the light in an air gap, since that could cause unwanted back reflection in the fiber system. Another type of attenuator utilizes a length of high-loss optical fiber, that operates upon its input optical signal power level in such a way that its output signal power level is less than the input level.

Types
Optical attenuators can take a number of different forms and are typically classified as fixed or variable attenuators. What's more, they can be classified as LC, SC, ST, FC, MU, E2000 etc. according to the different types of connectors.

Fixed Attenuators
Fixed optical attenuators used in fiber optic systems may use a variety of principles for their functioning. Preferred attenuators use either doped fibers, or mis-aligned splices, or total power since both of these are reliable and inexpensive. Inline style attenuators are incorporated into patch cables. The alternative build out style attenuator is a small male-female adapter that can be added onto other cables.

Non-preferred attenuators often use gap loss or reflective principles. Such devices can be sensitive to: modal distribution, wavelength, contamination, vibration, temperature, damage due to power bursts, may cause back reflections, may cause signal dispersion etc.

Loopback attenuators
Loopback fiber optic attenuator is designed for testing, engineering and the burn-in stage of boards or other equipment. Available in SC/UPC, SC/APC, LC/UPC, LC/APC, MTRJ, MPO for singlemode application.900 um fiber cable inside of the black shell for LC and SC type. No black shell for MTRJ and MPO type.

Built-in variable attenuators
Built-in variable optical attenuators may be either manually or electrically controlled. A manual device is useful for one-time set up of a system, and is a near-equivalent to a fixed attenuator, and may be referred to as an "adjustable attenuator". In contrast, an electrically controlled attenuator can provide adaptive power optimization.

Attributes of merit for electrically controlled devices, include speed of response and avoiding degradation of the transmitted signal. Dynamic range is usually quite restricted, and power feedback may mean that long term stability is a relatively minor issue. Speed of response is a particularly major issue in dynamically reconfigurable systems, where a delay of one millionth of a second can result in the loss of large amounts of transmitted data. Typical technologies employed for high speed response include liquid crystal variable attenuator (LCVA), or lithium niobate devices. There is a class of built-in attenuators that is technically indistinguishable from test attenuators, except they are packaged for rack mounting, and have no test display.

Variable optical test attenuators
Variable optical test attenuators generally use a variable neutral density filter. Despite relatively high cost, this arrangement has the advantages of being stable, wavelength insensitive, mode insensitive, and offering a large dynamic range. Other schemes such as LCD, variable air gap etc. have been tried over the years, but with limited success.

They may be either manually or motor controlled. Motor control give regular users a distinct productivity advantage, since commonly used test sequences can be run automatically.

Attenuator instrument calibration is a major issue. The user typically would like an absolute port to port calibration. Also, calibration should usually be at a number of wavelengths and power levels, since the device is not always linear. However a number of instruments do not in fact offer these basic features, presumably in an attempt to reduce cost. The most accurate variable attenuator instruments have thousands of calibration points, resulting in excellent overall accuracy in use.

Test automation
Test sequences that use variable attenuators can be very time-consuming. Therefore, automation is likely to achieve useful benefits. Both bench and handheld-style devices are available that offer such features.

title: Optical attenuator


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Optical axis

An optical axis is an imaginary line that passes through the geometrical center of an optical system such as a camera lens, microscope or telescopic sight. Lens elements often have rotational symmetry about the axis.

The optical axis defines the path along which light propagates through the system, up to first approximation. For a system composed of simple lenses and mirrors, the axis passes through the center of curvature of each surface, and coincides with the axis of rotational symmetry. The optical axis is often coincident with the system's mechanical axis, but not always, as in the case of off-axis optical systems.

For an optical fiber, the optical axis is along the center of the fiber core, and is also known as the fiber axis.

title: Optical axis