# Signal-to-noise ratio

(Redirected from Signal to noise ratio)

Signal-to-noise ratio (often abbreviated SNR or S/N) is meaningful both in the context of information theory and, informally, for Usenet or other newsgroup-like services.

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## Technical sense

Signal-to-noise ratio is an engineering term for the power ratio between a signal (meaningful information) and the background noise:

[itex]

\mathrm{SNR} = {P_\mathrm{signal} \over P_\mathrm{noise}} [itex]

Because many signals have a very wide dynamic range, SNRs are often expressed in terms of the logarithmic decibel scale. In decibels, the SNR is 20 times the base-10 logarithm of the amplitude ratio, or 10 times the logarithm of the power ratio:

[itex]

\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 ) [itex]

where P is average power and A is RMS amplitude.

Signal-to-noise ratios are 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 magnitude, such as 1.228 VRMS (+4 dBu).

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).

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. In general, higher signal to noise is better. (i.e. cleaner.)

## Digital signals

When using digital storage the number of bits of each value determines the signal-to-noise ratio. In this case the noise is the error signal caused by the quantisation of the signal, taking place in the analog to digital conversion. For n bit integers the dynamic range (DNR) is also determined. The formula is:

[itex]DNR = SNR = 6.02 n[itex]

Each extra quantisation bit reduces the level of the quantisation noise by roughly 6 dB.

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

[itex]DNR = 6.02 * 2^m[itex]

[itex]SNR = 6.02 * n[itex]

Other texts have defined the signal-to-noise ratio as

[itex]SNR = 10(2n-1)log(2)+10(3)[itex] or [itex]SNR = 6.02n + 1.76[itex]

for digital-to-analog converter outputs with a full-amplitude sine-wave signal.

### Notes

• Often special filters are used to weight the noise: DIN-A, DIN-B, DIN-C, DIN-D, CCIR-601, and 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.

## Informal use

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".

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