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, namely the Nyquist–Shannon sampling theorem.

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
  • Pink noise
  • Black noise
  • Gaussian noise
  • Flicker noise, with 1/f power spectrum
  • Brown noise or 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
• 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
  • Coil noise, audible and electronic, caused by vibrating inductors and transformers
  • 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
• 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

See also

• Anti-information
• Signal-to-noise statistic, a mathematical formula to measure the difference of two values relative to their standard deviations

References