Noise (signal processing)

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

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

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, that is 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

A long list of noise measures have 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 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

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 the noise in telecommunications
Noise-domain reflectometry, uses existing signals to find cable faults
Noise-immune cavity-enhanced optical heterodyne molecular spectroscopy

References

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

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[1] Vyacheslav Tuzlukov (2010), Signal Processing Noise, Electrical Engineering and Applied Signal Processing Series, CRC Press. 688 pages. ISBN 9781420041118

[Vladutescu2015-2] Viviana Vladutescu, Daniela. "Systems Engineering for Space Based Applications" (PDF). www.ieee.li. CAS IEEE Long Island Section. Retrieved 26 March 2023.