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Signal Noise Ratio	Ratio	Signal to noise ratio in the Free Online Encyclopedia

Signal to noise ratio

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

1 Technical sense
2 Digital signals
3 Informal use
4 See also

Technical sense

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

$\mathrm{SNR} = {P_\mathrm{signal} \over P_\mathrm{noise}}$

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 20 times the base-10 logarithm of the amplitude ratio, or 10 times the logarithm of the power ratio:

$\mathrm{SNR (dB)} = 10 \log_{10} \left ( {P_\mathrm{signal} \over P_\mathrm{noise}} \right ) = 20 \log_{10} \left ( {A_\mathrm{signal} \over A_\mathrm{noise}} \right )$

where P is average power and A is RMS amplitude. Both signal and noise power are measured within the system bandwidth.

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 magnitude, such as 1 kHz at 1.228 V_RMS (+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).

In image processing, the SNR of an image is usually defined as the ratio of the mean pixel value to the standard deviation of the pixel values. Related measures are the "contrast ratio" and the "contrast to noise ratio".

Digital signals

When using digital storage the number of bits of each value determines the maximum 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. The noise level is non-linear and signal-dependent. Different calculations exist for different noise models. The noise is modeled as an analog error signal being summed with the signal before quantization.

Fixed point

For n-bit integers with equal distance between quantization levels (uniform quantization) the dynamic range (DR) is also determined.

Assuming a uniform distribution of input signal values, the quantization noise is a uniformly-distributed random signal with a peak-to-peak amplitude of one quantization level. The formula is:

DR(dB) = SNR(dB) = 20log 10 (2 n)

This is the origin of statements like "16-bit audio has a dynamic range of 96 dB". Each extra quantisation bit reduces the level of the quantisation noise by roughly 6 dB.

Assuming a full-scale sine wave signal, the quantization noise approximates a sawtooth wave with peak-to-peak amplitude of one quantization level. In this case, the SNR is:

$\mathrm{SNR (dB)} = 10(2n-1) \cdot \log_{10}(2)+10\log_{10}(3) \approx 6.02 \cdot n + 1.761$

Floating point

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

$\mathrm{DR (dB)} = 6.02 \cdot 2^m$

$\mathrm{SNR (dB)} = 6.02 \cdot n$

See quantization noise and bit resolution.

Notes

Analog-to-digital converters have other sources of noise that decrease the SNR compared to the theoretical maximum from the idealized quantization noise.
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 P-P, which gave +9 dB more SNR for video.
It is more common to express SNR in digital systems using Eb/No (the Energy per bit per noise power spectral density).

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".