Noise (signal processing)

In signal processing, unwanted modifications to a signal

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In signal processing, noise is a general term for unwanted (and, in general, unknown) modifications that a signal may suffer during capture, storage, transmission, processing, or conversion.[1]

Sometimes the word is also used to mean signals that are random (unpredictable) and carry no useful information; even if they are not interfering with other signals or may have been introduced intentionally, as in comfort noise.

Noise reduction, the recovery of the original signal from the noise-corrupted one, is a very common goal in the design of signal processing systems, especially filters. The mathematical limits for noise removal are set by information theory.

## Types of noise

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Signal processing noise can be classified by its statistical properties (sometimes called the "color" of the noise) and by how it modifies the intended signal:

* Additive noise, gets added to the intended signal
* White noise
* Additive white Gaussian noise
* Black noise
* Gaussian noise
* Pink noise or flicker noise, with 1/f power spectrum
* Brownian noise, with 1/f2 power spectrum
* Contaminated Gaussian noise, whose PDF is a linear mixture of Gaussian PDFs
* Power-law noise
* Cauchy noise
* Multiplicative noise, multiplies or modulates the intended signal
* Quantization error, due to conversion from continuous to discrete values
* Poisson noise, typical of signals that are rates of discrete events
* Shot noise, e.g. caused by static electricity discharge
* Transient noise, a short pulse followed by decaying oscillations
* Burst noise, powerful but only during short intervals
* Phase noise, random time shifts in a signal

## Noise in specific kinds of signals

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Noise may arise in signals of interest to various scientific and technical fields, often with specific features:

* Noise (audio), such as "hiss" or "hum", in audio signals
* Background noise, due to spurious sounds during signal capture
* Comfort noise, added to voice communications to fill silent gaps
* Electromagnetically induced noise, audible noise due to electromagnetic vibrations in systems involving electromagnetic fields
* Noise (video), such as "snow"
* Noise (radio), such as "static", in radio transmissions
* Image noise, affects images, usually digital ones
* Salt and pepper noise or spike noise, scattered very dark or very light pixels
* Fixed pattern noise, tied to pixel sensors
* Shadow noise, made visible by increasing brightness or contrast
* Speckle noise, typical of radar imaging and interferograms
* Film grain in analog photography
* Compression artifacts or "mosquito noise" around edges in JPEG and other formats
* Noise (electronics) in electrical signals
* Johnson–Nyquist noise, in semiconductors
* Quantum noise
* Quantum 1/f noise, a disputed theory about quantum systems
* Generation-recombination noise, in semiconductor devices
* Oscillator phase noise, random fluctuations of the phase of an oscillator
* Barkhausen effect or Barkhausen noise, in the strength of a ferromagnet
* Spectral splatter or switch noise, caused by on/off transmitter switching
* Ground noise, appearing at the ground terminal of audio equipment
* Synaptic noise, observed in neuroscience
* Neuronal noise, observed in neuroscience
* Transcriptional noise in the transcription of genes to proteins
* Cosmic noise, in radioastronomy
* Phonon noise in materials science
* Internet background noise, packets sent to unassigned or inactive IP addresses
* Fano noise, in particle detectors
* Mode partition noise in optical cables
* Seismic noise, spurious ground vibrations in seismology
* Cosmic microwave background, microwave noise left over from the Big Bang

## Measures of noise in signals

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A long list of noise measures has been defined to measure noise in signal processing: in absolute terms, relative to some standard noise level, or relative to the desired signal level. They include:

* Dynamic range, often defined by inherent noise level
* Signal-to-noise ratio (SNR), ratio of noise power to signal power
* Peak signal-to-noise ratio, maximum SNR in a system
* Signal to noise ratio (imaging), for images
* Carrier-to-noise ratio, the signal-to-noise ratio of a modulated signal
* Noise power
* Noise figure
* Noise-equivalent flux density, a measure of noise in astronomy
* Noise floor
* Noise margin, by how much a signal exceeds the noise level
* Reference noise, a reference level for electronic noise
* Noise spectral density, noise power per unit of bandwidth
* Noise temperature
* Effective input noise temperature
* Noise-equivalent power, a measure of sensitivity for photodetectors
* Relative intensity noise, in a laser beam
* Antenna noise temperature, measure of noise in telecommunications antenna
* Received noise power, noise at a telecommunications receiver
* Circuit noise level, ratio of circuit noise to some reference level
* Channel noise level, some measure of noise in a communication channel
* Noise-equivalent target, intensity of a target when the signal-to-noise level is 1[2]
* Equivalent noise resistance, a measure of noise based on an equivalent resistor
* Carrier-to-receiver noise density, ratio of received carrier power to receiver noise
* Carrier-to-noise-density ratio,
* Spectral signal-to-noise ratio
* Antenna gain-to-noise temperature, a measure of antenna performance
* Contrast-to-noise ratio, a measure of image quality
* Noise print, statistical signature of ambient noise for its suppression
* Equivalent pulse code modulation noise, measure of noise by comparing to PCM quantization noise

## Technology for noise in signals

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Almost every technique and device for signal processing has some connection to noise. Some random examples are:

* Noise shaping
* Antenna analyzer or noise bridge, used to measure the efficiency of antennas
* Noise gate
* Noise generator, a circuit that produces a random electrical signal
* Radio noise source used to calibrate radiotelescopes
* Friis formulas for noise in telecommunications
* Noise-domain reflectometry, uses existing signals to find cable faults
* Noise-immune cavity-enhanced optical heterodyne molecular spectroscopy

## See also

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* Anti-information
* Noise (electronics)
* Signal-to-noise statistic, a mathematical formula to measure the difference of two values relative to their standard deviations

## References

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1. ^ Vyacheslav Tuzlukov (2010), Signal Processing Noise, Electrical Engineering and Applied Signal Processing Series, CRC Press. 688 pages. ISBN 9781420041118
2. ^ Viviana Vladutescu, Daniela. "Systems Engineering for Space Based Applications" (PDF). www.ieee.li. CAS IEEE Long Island Section. Retrieved 26 March 2023.