Signal-to-noise ratio

The phrase signal-to-noise ratio, often abbreviated SNR or S/N, is an engineering term for the ratio between the maximum possible signal (meaningful information) and the background noise. Because many signals have a very wide dynamic range, SNRs are often expressed in terms of the logarithmic decibel scale.

Often the signals being compared are electromagnetic in nature, though it is also possible to apply the term to sound and light stimuli.

Due to the definition of decibel the SNR gave the same result independent of the type of signal which is evaluated (power, current, voltage).

SNR is also usually taken to mean an average signal to noise ratio, as it is possible that (near) instantaneous signal to noise ratios will be considerably different.

The SNR in decibels is 20 times the base-10 logarithm of the amplitude ratio, or 10 times the logarithm of the power ratio. See decibel.

Higher signal to noise is better i.e. cleaner.

When using digital storage the number of bits of each value determines the signal-to-noise ratio. For n bit integers the dynamic range (DNR) is also determined. The formula is:

For floating point numbers, with n bits in the mantissa and m bits in the exponent:

Note

often special filters are used to weight the noise (DIN-A, DIN-B, DIN-C, DIN-D, CCIR-601, special filters in Video (Kammfilter)
maximum possible full scale signal can be charged as peak-to-peak or as RMS. Audio uses RMS, Video PP, which gave +9 dB more SNR for video.
In Audio Coding there are terms like
- NMT
- TMN
- SMR

SINAD: Abbreviation for signal-plus-noise-plus-distortion to noise-plus-distortion ratio.

The ratio of (a) total received power, i.e. , the received signal-plus-noise-plus-distortion power to (b) the received noise-plus-distortion power.
The ratio of (a) the recovered audio power, i.e., the original modulating audio signal plus noise plus distortion powers from a modulated radio frequency carrier to (b) the residual audio power, i.e., noise-plus-distortion powers remaining after the original modulating audio signal is removed.

Note: The SINAD is usually expressed in dB.

Source: from Federal Standard 1037C in support of MIL-STD-188

In common usage, "signal-to-noise ratio" describes the ratio of useful information to false or irrelevant information, for example in an online discussion forum.

The term has been used e.g. on Usenet, where off-topic posts and spam are regarded as "noise" that interferes with the "signal" of interesting discussion.

Many Internet users prefer moderated forums, for instance, because moderation can improve the SNR of a forum. The Wiki collaboration model addresses the same question in a different way, by granting every user the power to "moderate" content. The assumption is that a majority of users are motivated by belief in the project goals, which leads to improved SNR by making it easier to add "signal" than "noise".