Signal To Noise Ratio

Signal-to-noise ratio - Wikipedia, the free encyclopedia
Signal-to-noise ratio is closely related to the concept of dynamic range, where ... Main article: Signal to noise ratio (image processing) ...
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signal-to-noise ratio: Definition from Answers.com
signal-to-noise ratio ( ?sign?l t? ?nöiz ?r?sh? ) ( electronics ) The ratio of the amplitude of a desired signal at any point to the amplitude of
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Signal-to-noise ratio - Scholarpedia
The signal-to-noise ratio is typically written as SNR and equals. Signal-to-noise ratio is also defined for random ... Peak Signal-to-Noise Ratio (PSNR) ...
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Nikon MicroscopyU: Interactive Java Tutorials - CCD Signal-To-Noise Ratio
... of which must be considered in the signal-to-noise ratio calculation. ... Parameters that affect signal-to-noise ratio for a CCD sensor can be varied for ...
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Signal-to-noise ratio (often abbreviated SNR or S/N) is an electrical engineering concept defined as the ratio of a signal power to the noise power corrupting the signal.

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 (physics) ratio between a Signal (information theory) (meaningful information) and the background Signal 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 Root mean square amplitude. 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 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. 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).

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-distortion signal on a Channel (communications). 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 sound engineering, this reference signal is usually a sine wave, sounding a pitch (music), at a recognized and standardized nominal level or alignment level, such as 1 kHz at +4 dBu (1.228 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. Related measures are the Contrast ratio and the "contrast-to-noise ratio".
The connection between optical power and voltage in an imaging system is linear. This usually means that the SNR of the electrical signal is calculated by the 10 log rule. With an interferometer 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). 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.

For a measurement device generally speaking device that is poorly isolated in a mechanical point of view; the middle of the curve shows a lower noise, due to a lesser surrounding human activity at night.

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.

If we process a Fourier transform on the recorded signal, random noise corresponds to high frequencies: there are variations between two neighbouring points. If the signal is made of broad peaks, then these peaks correspond to low frequencies; the "highest frequency" can be estimated by inverse of the width of the peak.

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 (signal processing) of the signal, taking place in the analog-to-digital converter. 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 (Quantization (signal processing)) 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, 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 Defining and Testing Dynamic Parameters in High-Speed ADCs — Maxim Integrated Products Application note 728 and uniform distribution. 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. 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. Fixed-Point vs. Floating-Point DSP for Superior Audio — Rane Corporation technical library

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 - comb filter.
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/N0 - the energy per bit per noise power spectral density.

Informal use Informally, "signal-to-noise ratio" refers to the ratio of useful information to false or irrelevant data.

In internet forum such as Usenet, off-topic posts and spamming are regarded as "noise" that interferes with the "signal" of appropriate discussion. Another example is Bugzilla, where "please fix this" comments clutter up the discussion without helping to solve the bug. A system of moderation system may improve the SNR by filtering out irrelevant posts.

The wiki collaboration model addresses the same problem in a different way, by permitting users to "moderate" content, ideally adding signal while removing noise.

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)
Carrier-to-receiver noise density (C/N0)
Carrier-to-Interference Ratio (CIR or C/I)
Carrier-to-Noise-and-Interference Ratio (CIR or C/I)
CNR (imaging)
SQNR (Signal-to-Quantization Noise Ratio)
Total harmonic distortion
Noise figure

References

Introduction to DSP: Quantisation - Bores Signal Processing

External links

ADC and DAC Glossary - Maxim Integrated Products
Understand SINAD, ENOB, SNR, THD, THD + N, and SFDR so you don't get lost in the noise floor - Analog Devices
The Relationship of dynamic range to data word size in digital audio processing
Calculation of signal-to-noise ratio, noise voltage, and noise level
Learning by simulations - a simulation showing the improvement of the SNR by time averaging
Dynamic Performance Testing of Digital Audio D/A Converters

signal-to-noise ratio from FOLDOC
signal-to-noise ratio. 1. < communications > (SNR, "s/n ratio", "s:n ratio") "Signal" refers to useful information conveyed by some communications medium, and "noise" to anything ...

signal-to-noise ratio from FOLDOC
S/N ratio ==> signal-to-noise ratio. 1. < communications > (SNR, "s/n ratio", "s:n ratio") "Signal" refers to useful information conveyed by some communications medium, and "noise ...

Signal-to-noise ratio - Wikipedia, the free encyclopedia
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 and ...

Definition: signal-to-noise ratio from Online Medical Dictionary
The Online Medical Dictionary is a searchable dictionary of definitions from medicine, science and technology.

AskOxford: signal-to-noise ratio
signal-to-noise ratio • noun the ratio of the strength of an electrical or other signal carrying information to that of unwanted interference, generally expressed in decibels.

What is signal-to-noise ratio? - a definition from Whatis.com - see ...
In analog and digital communications, signal-to-noise ratio, often written S/N or SNR, is a measure of signal strength relative to background noise.

Signal-to-Noise Ratio
Leeds X-ray Imaging Research. Digital Image Quality, Evaluation and Enhancement

Signal-noise ratio - Hutchinson encyclopedia article about Signal ...
Ratio of the power of an electrical signal to that of the unwanted noise accompanying the signal. It is expressed in decibels.

signal/noise ratio - Hutchinson encyclopedia article about signal ...
Ratio of the power of an electrical signal to that of the unwanted noise accompanying the signal. It is expressed in decibels.

signal-to-noise ratio
signal-to-noise ratio: n. [from analog electronics] Used by hackers in a generalization of its technical meaning. ‘Signal’ refers to useful information conveyed by some ...