Signal-to-noise ratio (often abbreviated SNR or S/N) is an electrical engineering measurement, also used in other fields (such as scientific measurement or biological cell signaling), defined as the ratio of a signal power to the noise power corrupting the signal. A ratio higher than 1:1 indicates more signal than noise.

In less technical terms, signal-to-noise 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

In engineering, signal-to-noise ratio is a term for the power ratio between a signal (meaningful information) and the background noise:
\mathrm{SNR} = {P_\mathrm{signal} \over P_\mathrm{noise}},
where P is average power. Both signal and noise power must be measured at the same or equivalent points in a system, and within the same system bandwidth. If the signal and the noise are measured across the same impedance, then the SNR can be obtained by calculating the square of the amplitude ratio:
\mathrm{SNR} = {P_\mathrm{signal} \over P_\mathrm{noise}} = \left ( {A_\mathrm{signal} \over A_\mathrm{noise} } \right )^2,
where A is root mean square (RMS) amplitude (for example, typically, RMS voltage). 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:
\mathrm{SNR (dB)} = 10 \log_{10} \left ( {P_\mathrm{signal} \over P_\mathrm{noise}} \right ) = 20 \log_{10} \left ( {A_\mathrm{signal} \over A_\mathrm{noise}} \right ) = {P_\mathrm{signal,dB} - P_\mathrm{noise,dB}}.
 

Alternate forms

A common alternative definition of SNR is the ratio of mean to standard deviation of a signal or measurement:[1][2]
SNR = μ / σ
where μ is the signal, or the mean or expected value of the signal, or some measure of signal strength, and σ is the standard deviation of the noise, or an estimate thereof. The exact methods may vary between fields. For example, if the signal data are known to be constant, then σ can be calculated using the standard deviation of the signal. If the signal data are not constant, then σ can be calculated from data where the signal is zero or relatively constant.

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).
Signal-to-noise ratio is closely related to the concept of dynamic range, where dynamic range measures the ratio between noise and the greatest un-distorted 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 signal-to-noise 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 VRMS).
SNR is usually taken to indicate an average signal-to-noise ratio, as it is possible that (near) instantaneous signal-to-noise 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'.