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Encyclopedia > 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 magnitude of a signal (meaningful information) and the magnitude of background noise. Because many signals have a very wide dynamic range, SNRs are often expressed in terms of the logarithmic decibel scale.

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.

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 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 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. 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:

DNR = SNR = 6.02n

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:

DNR = 6.02 * 2m

SNR = 6.02 * n

### Note

• 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.
• In Audio Coding there are terms like

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

1. 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.
2. 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".

Here's a slight caveat: Signal to noise has several different technical definitions but always refers to one concept in general: How much signal you have over some type of noise. The noise can originate in the detector that you are using to make your observation. It might also be a general "noise", e.g. a background that includes not only your detector but a physical background that is related to whatever it is you are measuring. It can be defined by using the logarithmic definition above, or it might be a simple ratio. It is a vague definition at best and pretty much always confusing.

The reader is advised to be sure in using the right formula for their specific application.

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