Signal-to-noise ratio (often abbreviated SNR or S/N) is an electrical engineering concept, also used in other fields (such as scientific measurements, biological cell signaling), defined as the ratio of a signal power to the noise power corrupting the signal. Electrical engineering, sometimes referred to as electrical and electronic engineering, is a field of Engineering that deals with the study and application of Measurement is the process of estimating the magnitude of some attribute of an object such as its length or weight relative to some standard ( unit of measurement) such as Cell signaling is part of a Complex system of Communication that governs basic cellular activities and coordinates cell actions

In less technical terms, signal-to-noise ratio compares the level of a desired signal (such as music) to the level of background noise. The higher the ratio, the less obtrusive the background noise is.

## Technical sense

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

$\mathrm{SNR} = {P_\mathrm{signal} \over P_\mathrm{noise}} = \left ( {A_\mathrm{signal} \over A_\mathrm{noise} } \right )^2$

where P is average power and A is RMS amplitude. In Physics, power (symbol P) is the rate at which work is performed or energy is transmitted or the amount of energy required or expended for In the fields of communications, Signal processing, and in Electrical engineering more generally a signal is any time-varying or spatial-varying quantity In Science, and especially in Physics and Telecommunication, noise is fluctuations in and the addition of external factors to the stream of target In Mathematics, the root mean square (abbreviated RMS or rms) also known as the quadratic mean, is a statistical measure of the Both signal and noise power (or amplitude) must be measured at the same or equivalent points in a system, and within the same system bandwidth.

Because many signals have a very wide dynamic range, SNRs are usually expressed in terms of the logarithmic decibel scale. In Mathematics, the logarithm of a number to a given base is the power or Exponent to which the base must be raised in order to produce The decibel ( dB) is a logarithmic unit of measurement that expresses the magnitude of a physical quantity (usually power or intensity relative to In decibels, the SNR is, by definition, 10 times the logarithm of the power ratio. If the signal and the noise is measured across the same impedance then the SNR can be obtained by calculating 20 times the base-10 logarithm of the amplitude ratio:

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

### Electrical SNR and acoustics

Often the signals being compared are electromagnetic in nature, though it is also possible to apply the term to sound stimuli. The decimal ( base ten or occasionally denary) Numeral system has ten as its base. In Mathematics, the logarithm of a number to a given base is the power or Exponent to which the base must be raised in order to produce Amplitude is the magnitude of change in the oscillating variable with each Oscillation, within an oscillating system Electromagnetism is the Physics of the Electromagnetic field: a field which exerts a Force on particles that possess the property of Sound' is Vibration transmitted through a Solid, Liquid, or Gas; particularly sound means those vibrations composed of Frequencies 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). The decibel ( dB) is a logarithmic unit of measurement that expresses the magnitude of a physical quantity (usually power or intensity relative to

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. Dynamic range is a term used frequently in numerous fields to describe the Ratio between the smallest and largest possible values of a changeable quantity such as in Sound A distortion is the alteration of the original shape (or other characteristic of an object image sound waveform or other form of information or representation Channel, in communications (sometimes called communications channel) refers to the medium used to convey Information from a 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 nominal level or alignment level, such as 1 kHz at +4 dBu (1. Sound' is Vibration transmitted through a Solid, Liquid, or Gas; particularly sound means those vibrations composed of Frequencies Engineering is the Discipline and Profession of applying technical and scientific Knowledge and Pitch represents the perceived Fundamental frequency of a sound Nominal level is the operating level at which an electronic Signal processing device is designed to operate The alignment level in an audio signal chain or on an audio recording is a defined anchor point that represents a reasonable or typical level The decibel ( dB) is a logarithmic unit of measurement that expresses the magnitude of a physical quantity (usually power or intensity relative to 228 VRMS).

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 concept can be understood as normalizing the noise level to 1 (0 dB) and measuring how far the signal 'stands out'. In general, higher signal to noise is better; the signal is 'cleaner'.

### Image processing and interferometry

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. An image (from Latin imago) or picture is an artifact usually two-dimensional that has a similar appearance to some subject &mdashusually In Statistics, mean has two related meanings the Arithmetic mean (and is distinguished from the Geometric mean or Harmonic mean In Probability and Statistics, the standard deviation is a measure of the dispersion of a collection of values Related measures are the "contrast ratio" and the "contrast-to-noise ratio". The contrast ratio is a measure of a display system defined as the Ratio of the Luminance of the brightest color (white to that of the darkest color (black that
The connection between optical power and voltage in an imaging system is linear. Optical power ( dioptric power or refractive power) is the degree to which a lens or Mirror converges or diverges light Electrical tension (or voltage after its SI unit, the Volt) is the difference of electrical potential between two points of an electrical This usually means that the SNR of the electrical signal is calculated by the 10 log rule. With an interferometric system, however, where interest lies in the signal from one arm only, the field of the electromagnetic wave is proportional to the voltage (assuming that the intensity in the second, the reference arm is constant). Interferometry is the technique of using the pattern of Interference created by the superposition of two or more Waves to diagnose the properties of Therefore the optical power of the measurement arm is directly proportional to the electrical power and electrical signals from optical interferometry are following the 20 log rule.

The Rose criterion (named after Albert Rose) states that an SNR of at least 5 is needed to be able to distinguish image features at 100% certainty. Albert Rose (born New York City, 30 March 1910, died on 26 July 1990) was an American physicist who made major contributions An SNR less than 5 means less than 100% certainty in identifying image details. [1]

### For measurement devices in general

Recording of the noise of a thermogravimetric analysis device that is poorly isolated from a mechanical point of view; the middle of the curve shows a lower noise, due to a lesser surrounding human activity at night. Thermogravimetric Analysis or TGA is a type of testing that is performed on samples to determine changes in Weight in relation to change in Temperature

Any measurement device is disturbed by parasitic phenomena. This includes the electronic noise as described above, but also any external event that affects the measured phenomenon — wind, vibrations, gravitational attraction of the moon, variations of temperature, variations of humidity etc. depending on what is measured and of the sensitivity of the device.

It is often possible to reduce the noise by controlling the environment. Otherwise, when the characteristics of the noise are known and are different from the signal's, it is possible to filter it or to process the signal.

When the noise is a random perturbation and the signal is a constant value, it is possible to enhance the SNR by increasing the measurement time.

## 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 quantization of the signal, taking place in the analog-to-digital conversion. is a one volume manga created by Tsutomu Nihei as a prequel to his ten-volume work Blame!. The word error has different meanings and usages relative to how it is conceptually applied In Digital signal processing, quantization is the process of approximating a continuous range of values (or a very large set of possible discrete values by a relatively-small An analog-to-digital converter (abbreviated ADC, A/D or A to D) is an electronic integrated circuit which converts continuous signals to The noise level is non-linear and signal-dependent; different calculations exist for different signal models. The noise is modeled as an analog error signal being summed with the signal before quantization ("additive noise").

The modulation error ratio (MER) is a measure of the SNR in a digitally modulated signal. Like SNR, MER can be expressed in dB.

### Fixed point

For n-bit integers with equal distance between quantization levels (uniform quantization) the dynamic range (DR) is also determined. In Computing, a fixed-point number representation is a Real data type for a number that has a fixed number of digits after (and sometimes also before the In Digital signal processing, quantization is the process of approximating a continuous range of values (or a very large set of possible discrete values by a relatively-small Dynamic range is a term used frequently in numerous fields to describe the Ratio between the smallest and largest possible values of a changeable quantity such as in Sound

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, making the amplitude ratio 2n/1. The formula is then:

$\mathrm{DR (dB)} = \mathrm{SNR (dB)} = 20 \log_{10}(2^n) \approx 6.02 \cdot n$

This relationship is the origin of statements like "16-bit audio has a dynamic range of 96 dB". Each extra quantization bit increases the dynamic range by roughly 6 dB.

Assuming a full-scale sine wave signal (that is, the quantizer is designed such that it has the same minimum and maximum values as the input signal), the quantization noise approximates a sawtooth wave with peak-to-peak amplitude of one quantization level[2] and uniform distribution. In electronics and signal processing full scale or full code represents the maximum amplitude a system can present The sawtooth wave (or saw wave) is a kind of Non-sinusoidal waveform. In this case, the SNR is approximately

$\mathrm{SNR (dB)} \approx 20 \log_{10} (2^n \sqrt {3/2}) \approx 6.02 \cdot n + 1.761$

### Floating point

Floating-point numbers provide a way to trade off signal-to-noise ratio for an increase in dynamic range. In Computing, floating point describes a system for numerical representation in which a string of digits (or Bits represents a Real number. For n bit floating-point numbers, with n-m bits in the mantissa and m bits in the exponent:

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

Note that the dynamic range is much larger than fixed-point, but at a cost of a worse signal-to-noise ratio. This makes floating-point preferable in situations where the dynamic range is large or unpredictable. Fixed-point's simpler implementations can be used with no signal quality disadvantage in systems where dynamic range is less than 6. 02m. The very large dynamic range of floating-point can be a disadvantage, since it requires more forethought in designing algorithms. [3]

### Notes

• Analog-to-digital converters have other sources of noise that decrease the SNR compared to the theoretical maximum from the idealized quantization noise. An analog-to-digital converter (abbreviated ADC, A/D or A to D) is an electronic integrated circuit which converts continuous signals to
• Often special filters are used to weight the noise: DIN-A, DIN-B, DIN-C, DIN-D, CCIR-601; for video, special filters such as comb filters may be used. In Signal processing, a comb filter adds a delayed version of a signal to itself causing constructive and destructive interference.
• 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. E b/ N 0 (the energy per bit to noise power spectral density ratio) is an important parameter in Digital communication or
Further information: Quantization noise, Bit resolution

## Informal use

Informally, "signal-to-noise ratio" refers to the ratio of useful information to false or irrelevant data. The difference between the actual analog value and quantized digital value due is called quantization error.

In online discussion forums such as Usenet, off-topic posts and spam are regarded as "noise" that interferes with the "signal" of appropriate discussion. An, or message board, is a Bulletin board system in the form of a discussion site Usenet, a Portmanteau of "user" and "network" is a world-wide distributed Internet discussion system A contribution is on-topic if it is within the bounds of the current discussion and off-topic if not Spamming is the abuse of electronic messaging systems to indiscriminately send unsolicited bulk messages Another example is Bugzilla, where "please fix this" comments clutter up the discussion without helping to solve the bug. Bugzilla is a Web -based general-purpose Bugtracker tool originally developed and used by the Mozilla project and licensed under the [1] A system of moderation may improve the SNR by filtering out irrelevant posts. On Internet Websites which invite users to post comments a moderation system is the method the Webmaster chooses to sort contributions which are irrelevant

The wiki collaboration model addresses the same problem in a different way, by permitting users to "moderate" content, ideally adding signal while removing noise. A wiki is a page or collection of Web pages designed to enable anyone who accesses it to contribute or modify content using a simplified Markup language.

## See also

• Audio system measurements
• Video quality
• Subjective video quality
• Near-far problem
• Peak signal-to-noise ratio
• SINAD (ratio of signal-including-noise-and-distortion to noise-and-distortion only)
• ENOB
• Eb/N0
• Es/N0
• Carrier to Noise Ratio (CNR or C/N)
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