# Signal:noise

Signal-to-noise ratio (abbreviated SNR, S/N, or S:N) is a measure in science and engineering that compares the level of a desired signal relative to the background noise. It is defined as the ratio of signal power to noise power. A ratio greater to one indicates that there is more signal than noise. Signal-to-noise ratio is commonly used to describe electrical signals and time series, but can be used to describe any measurement with a blend of useful information and unwanted noise.

## Definition

Signal-to-noise ratio is defined as the power ratio between a signal (meaningful information) and the background noise (unwanted signal):

${\displaystyle \mathrm {S:N} ={\frac {P_{\mathrm {signal} }}{P_{\mathrm {noise} }}},}$

where P is average power. Both signal and noise power must be measured at the same or equivalent points in a time series. The SNR can be obtained by calculating the square of the amplitude ratio:

${\displaystyle \mathrm {S:N} ={\frac {P_{\mathrm {signal} }}{P_{\mathrm {noise} }}}=\left({\frac {A_{\mathrm {signal} }}{A_{\mathrm {noise} }}}\right)^{2},}$

where A is root mean square (RMS) amplitude. Because many signals have a very wide dynamic range, SNRs are often expressed using the logarithmic decibel scale. In decibels, the SNR is defined as

${\displaystyle \mathrm {S:N_{dB}} =10\log _{10}\left({\frac {P_{\mathrm {signal} }}{P_{\mathrm {noise} }}}\right)={P_{\mathrm {signal,dB} }-P_{\mathrm {noise,dB} }},}$

which may equivalently be written using amplitude ratios as

${\displaystyle \mathrm {S:N_{dB}} =10\log _{10}\left({\frac {A_{\mathrm {signal} }}{A_{\mathrm {noise} }}}\right)^{2}=20\log _{10}\left({\frac {A_{\mathrm {signal} }}{A_{\mathrm {noise} }}}\right).}$