# Signal-to-noise ratio

signal to noise ratioSNRsignal-to-noisesignal levelnoisesignal to noiseS/NS/N ratioSignal to noise ratio (image processing)signal-to-noise-ratio
Signal-to-noise ratio (abbreviated SNR or S/N) is a measure used in science and engineering that compares the level of a desired signal to the level of background noise.wikipedia
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### Noise (signal processing)

noisenoisybackground noise
Signal-to-noise ratio (abbreviated SNR or S/N) is a measure used in science and engineering that compares the level of a desired signal to the level of background noise.

### Decibel

dBdecibelsbel
SNR is defined as the ratio of signal power to the noise power, often expressed in decibels. Because many signals have a very wide dynamic range, signals are often expressed using the logarithmic decibel scale. In audio engineering, the reference signal is usually a sine wave at a standardized nominal or alignment level, such as 1 kHz at +4 dBu (1.228 V RMS ).
In electronics, the gains of amplifiers, attenuation of signals, and signal-to-noise ratios are often expressed in decibels.

### Channel capacity

capacitydata capacityinformation capacity
The signal-to-noise ratio, the bandwidth, and the channel capacity of a communication channel are connected by the Shannon–Hartley theorem.
An application of the channel capacity concept to an additive white Gaussian noise (AWGN) channel with B Hz bandwidth and signal-to-noise ratio S/N is the Shannon–Hartley theorem:

### Dynamic range

DRdynamicdynamic and tonal range
Because many signals have a very wide dynamic range, signals are often expressed using the logarithmic decibel scale.
Dynamic range is therefore the signal-to-noise ratio (SNR) for the case where the signal is the loudest possible for the system.

### Nominal level

nominalnominal signal level
In audio engineering, the reference signal is usually a sine wave at a standardized nominal or alignment level, such as 1 kHz at +4 dBu (1.228 V RMS ).
In audio, a related measurement, signal-to-noise ratio, is usually defined as the difference between the nominal level and the noise floor, leaving the headroom as the difference between nominal and maximum output.

### Shannon–Hartley theorem

Shannon-Hartley theoremHartley's lawShannon limit
The signal-to-noise ratio, the bandwidth, and the channel capacity of a communication channel are connected by the Shannon–Hartley theorem.

### Noise (electronics)

noiseelectronic noiseelectrical noise
Signal-to-noise ratio is defined as the ratio of the power of a signal (meaningful information) to the power of background noise (unwanted signal):
Noise is, however, typically distinguished from interference, for example in the signal-to-noise ratio (SNR), signal-to-interference ratio (SIR) and signal-to-noise plus interference ratio (SNIR) measures.

### Low-noise amplifier

Additionally, internal noise of electronic systems can be reduced by low-noise amplifiers.
A low-noise amplifier (LNA) is an electronic amplifier that amplifies a very low-power signal without significantly degrading its signal-to-noise ratio.

### Logarithm

logarithmsloglogarithmic function
Because many signals have a very wide dynamic range, signals are often expressed using the logarithmic decibel scale.
The signal-to-noise ratio describing the amount of unwanted noise in relation to a (meaningful) signal is also measured in decibels.

### Communication channel

channelchannelscommunications channel
The signal-to-noise ratio, the bandwidth, and the channel capacity of a communication channel are connected by the Shannon–Hartley theorem.

### Eb/N0

E b /N 0 Eb/NoE b /N 0 ratio
Although noise levels in a digital system can be expressed using SNR, it is more common to use E b /N o, the energy per bit per noise power spectral density.
In digital communication or data transmission, E b /N 0 (energy per bit to noise power spectral density ratio) is a normalized signal-to-noise ratio (SNR) measure, also known as the "SNR per bit".

### Analog-to-digital converter

Real analog-to-digital converters also have other sources of noise that further decrease the SNR compared to the theoretical maximum from the idealized quantization noise, including the intentional addition of dither.
The performance of an ADC is primarily characterized by its bandwidth and signal-to-noise ratio (SNR).

### Lock-in amplifier

phase-sensitive detectorlock-indemodulated
For example, it is sometimes possible to use a lock-in amplifier to modulate and confine the signal within a very narrow bandwidth and then filter the detected signal to the narrow band where it resides, thereby eliminating most of the broadband noise.
The device is often used to measure phase shift, even when the signals are large, have a high signal-to-noise ratio and do not need further improvement.

### Signal

signalselectrical signalsignaling
Signal-to-noise ratio (abbreviated SNR or S/N) is a measure used in science and engineering that compares the level of a desired signal to the level of background noise. Signal-to-noise ratio is defined as the ratio of the power of a signal (meaningful information) to the power of background noise (unwanted signal):

### Matched filter

matched filteringmatched-filteringNorth filters
The matched filter is the optimal linear filter for maximizing the signal-to-noise ratio (SNR) in the presence of additive stochastic noise.

### Signal-to-interference-plus-noise ratio

Signal-to-noise plus interferencesignal-to-interference and noise ratio (SINR)signal-to-interference-and-noise
SINR is the Signal-to-noise-plus-interference ratio.
Analogous to the signal-to-noise ratio (SNR) used often in wired communications systems, the SINR is defined as the power of a certain signal of interest divided by the sum of the interference power (from all the other interfering signals) and the power of some background noise.

### Coefficient of variation

CVRelative standard deviationcoefficients of variation
An alternative definition of SNR is as the reciprocal of the coefficient of variation, i.e., the ratio of mean to standard deviation of a signal or measurement:
In signal processing, particularly image processing, the reciprocal ratio \mu/\sigma is referred to as the signal to noise ratio in general and signal-to-noise ratio (imaging) in particular.

### Film speed

ISOISO sensitivityASA
Yet another alternative, very specific, and distinct definition of SNR is employed to characterize sensitivity of imaging systems; see Signal-to-noise ratio (imaging).
The noise-based speed is defined as the exposure that will lead to a given signal-to-noise ratio on individual pixels.

signal-to-noise and distortionsignal-to-noise and distortion ratioSignal-to-noise-and-distortion
Note that with this definition, unlike SNR, a SINAD reading can never be less than 1 (i.e. it is always positive when quoted in dB).

### Audio system measurements

Audio quality measurementAudio noise measurementaudio performance

### Phase-shift keying

QPSKBPSKPSK
For instance an OSNR of 20 dB/0.1 nm could be given, even the signal of 40 GBit DPSK would not fit in this bandwidth.
If the signal-to-noise ratio is high (as is necessary for practical QPSK systems) the probability of symbol error may be approximated:

### Modulation error ratio

The modulation error ratio (MER) is a measure of the SNR in a digitally modulated signal.
MER is also closely related to signal-to-noise ratio.

### Video quality

qualityfull reference metricmodels
Among the oldest FR metrics are signal-to-noise ratio (SNR) and peak signal-to-noise ratio (PSNR), which are calculated between every frame of the original and the degraded video signal.

### Near–far problem

near-far problemnear-far
Since one transmission's signal is the other's noise, the signal-to-noise ratio (SNR) for the further transmitter is much lower.

### Generation loss

digital generation lossa copy of a copy may not be as 'sharp' as the originalcopies of analog recordings tend to degrade when copied
Digital resampling such as image scaling, and other DSP techniques can also introduce artifacts or degrade signal-to-noise ratio (S/N ratio) each time they are used, even if the underlying storage is lossless.