From Wikipedia, the free encyclopedia
Signaltonoise ratio (often abbreviated SNR or S/N) is an electrical engineering concept defined as the ratio of a signal power to the noise power corrupting the signal.
In less technical terms, signaltonoise ratio compares the level of a desired signal (such as music) to the level of background noise. The higher the ratio, the less obtrusive the background noise is.
Technical sense
Signaltonoise ratio is an engineering term for the power ratio between a signal (meaningful information) and the background noise:

where P is average power and A is RMS amplitude. Both signal and noise power (or amplitude) must be measured at the same or equivalent points in a system, and within the same system bandwidth.
Because many signals have a very wide dynamic range, SNRs are usually expressed in terms of the logarithmic decibel scale. In decibels, the SNR is, by definition, 10 times the logarithm of the power ratio. If the signal and the noise is measured across the same impedance then the SNR can be obtained by calculating 20 times the base10 logarithm of the amplitude ratio:

Electrical SNR and acoustics
Often the signals being compared are electromagnetic in nature, though it is also possible to apply the term to sound stimuli. Due to the definition of decibel, the SNR gives the same result independent of the type of signal which is evaluated (such as power, current, or voltage).
Signaltonoise ratio is closely related to the concept of dynamic range, where dynamic range measures the ratio between noise and the greatest undistorted signal on a channel. SNR measures the ratio between noise and an arbitrary signal on the channel, not necessarily the most powerful signal possible. Because of this, measuring signaltonoise ratios requires the selection of a representative or reference signal. In audio engineering, this reference signal is usually a sine wave, sounding a tone, at a recognized and standardized nominal level or alignment level, such as 1 kHz at +4 dBu (1.228 V_{RMS}).
SNR is usually taken to indicate an average signaltonoise ratio, as it is possible that (near) instantaneous signaltonoise ratios will be considerably different. The concept can be understood as normalizing the noise level to 1 (0 dB) and measuring how far the signal 'stands out'. In general, higher signal to noise is better; the signal is 'cleaner'.
Image processing and interferometry
In image processing, the SNR of an image is usually defined as the ratio of the mean pixel value to the standard deviation of the pixel values. Related measures are the "contrast ratio" and the "contrasttonoise ratio".
The connection between optical power and voltage in an imaging system is linear. This usually means that the SNR of the electrical signal is calculated by the 10 log rule. With an interferometric system, however, where interest lies in the signal from one arm only, the field of the electromagnetic wave is proportional to the voltage (assuming that the intensity in the second, the reference arm is constant). Therefore the optical power of the measurement arm is directly proportional to the electrical power and electrical signals from optical interferometry are following the 20 log rule.
For a measurement device generally speaking
Recording of the noise of a thermogravimetric analysis device that is poorly isolated in a mechanical point of view; the middle of the curve shows a lower noise, due to a lesser surrounding human activity at night.
Any measurement device is disturbed by parasitic phenomena. This includes the electronic noise as described above, but also any external event that affects the measured phenomenon — wind, vibrations, gravitational attraction of the moon, variations of temperature, variations of humidity etc. depending on what is measured and of the sensitivity of the device.
It is often possible to reduce the noise by controlling the environment. Otherwise, when the characteristics of the noise are known and are different from the signal's, it is possible to filter it or to process the signal.
When the noise is a random perturbation and the signal is a constant value, it is possible to enhance the SNR by increasing the measurement time.
If we process a Fourier transform on the recorded signal, random noise corresponds to high frequencies: there are variations between two neighbouring points. If the signal is made of broad peaks, then these peaks correspond to low frequencies; the "highest frequency" can be estimated by inverse of the width of the peak.
Digital signals
When using digital storage the number of bits of each value determines the maximum signaltonoise ratio. In this case the noise is the error signal caused by the quantization of the signal, taking place in the analogtodigital conversion. The noise level is nonlinear and signaldependent; different calculations exist for different signal models. The noise is modeled as an analog error signal being summed with the signal before quantization ("additive noise").
The modulation error ratio (MER) is a measure of the SNR in a digitally modulated signal. Like SNR, MER can be expressed in dB.
Fixed point
 See also: Fixed point
For nbit integers with equal distance between quantization levels (uniform quantization) the dynamic range (DR) is also determined.
Assuming a uniform distribution of input signal values, the quantization noise is a uniformlydistributed random signal with a peaktopeak amplitude of one quantization level, making the amplitude ratio 2^{n}/1. The formula is then:

This is the origin of statements like "16bit audio has a dynamic range of 96 dB".Each extra quantisation bit increases the dynamic range by roughly 6 dB. Assuming a fullscale sine wave signal, the quantization noise approximates a sawtooth wave with peaktopeak amplitude of one quantization level.^{[1]} In this case, the SNR is:

(With this signal model, 16bit audio has an SNR of 98.1 dB.)
Each extra quantisation bit increase the SNR (or reduces the level of the quantisation noise) by roughly 6 dB.
Floating point
Floatingpoint numbers provide a way to trade off signaltonoise ratio for an increase in dynamic range. For n bit floatingpoint numbers, with nm bits in the mantissa and m bits in the exponent:


Note that the dynamic range is much larger than fixedpoint, but at a cost of a worse signaltonoise ratio. This makes floatingpoint preferable in situations where the dynamic range is large or unpredictable. Fixedpoint's simpler implementations can be used with no signal quality disadvantage in systems where dynamic range is less than 6.02m. The very large dynamic range of floatingpoint can be a disadvantage, since it requires more forethought in designing algorithms.^{[2]}
Notes
 Analogtodigital converters have other sources of noise that decrease the SNR compared to the theoretical maximum from the idealized quantization noise.
 Often special filters are used to weight the noise: DINA, DINB, DINC, DIND, CCIR601, and special filters in video  comb filter.
 Maximum possible full scale signal can be charged as peaktopeak or as RMS. Audio uses RMS, Video PP, which gave +9 dB more SNR for video.
 It is more common to express SNR in digital systems using Eb/No  the energy per bit per noise power spectral density.
 Further information: Quantization noise, Bit resolution
Informal use
Informally, "signaltonoise ratio" refers to the ratio of useful information to false or irrelevant data.
In online discussion forums such as Usenet, offtopic posts and spam are regarded as "noise" that interferes with the "signal" of appropriate discussion, or Bugzilla, where "please fix this" comments clutter up the discussion without helping to solve the bug.[1] A system of moderation may improve the SNR by filtering out irrelevant posts.
The wiki collaboration model addresses the same problem in a different way, by permitting users to "moderate" content, ideally adding signal while removing noise. Unfortunately, the inverse often occurs when some users add noise and remove signals from articles.
See also
 Audio system measurements
 Video quality
 Subjective video quality
 Nearfar problem
 Peak signaltonoise ratio
 SINAD (ratio of signalplusnoiseplusdistortion to noiseplusdistortion)
 ENOB
 Eb/N0
 Carrier to Noise Ratio
 Carriertoreceiver noise density
 Contrast to Noise Ratio
 SQNR (SignaltoQuantization Noise Ratio)
References
 ^ Defining and Testing Dynamic Parameters in HighSpeed ADCs — Maxim IC Application note 728
 ^ FixedPoint vs. FloatingPoint DSP for Superior Audio — Rane Corporation technical library
 Introduction to DSP: Quantisation  Bores Signal Processing
External links
 ADC and DAC Glossary  Maxim IC
 Understand SINAD, ENOB, SNR, THD, THD + N, and SFDR so you don't get lost in the noise floor  Analog Devices
 The Relationship of dynamic range to data word size in digital audio processing
 Calculation of signaltonoise ratio, noise voltage, and noise level
 Learning by simulations  a simulation showing the improvement of the SNR by time averaging
 Dynamic Performance Testing of Digital Audio D/A Converters
Categories: Electronics terms  Noise  Digital audio  Engineering ratios  Measurement