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Signal-to-noise ratio (SNR, also written S/N) is the comparison of a desired signal with the noise that exists alongside it. In the common engineering form, it is the ratio of signal power to noise power. A higher SNR means the signal is stronger relative to the noise, under the measurement conditions that were stated. An SNR figure on its own tells you little until you know what was counted as signal, what was counted as noise, and where and how each was measured.
The basic definition
SNR describes how well a wanted signal stands out from unwanted noise. It is a ratio, not an absolute level. A recording with a loud voice and a quiet hiss has a high SNR; the same voice on top of a loud hum has a low one, even though the voice itself is identical. That is why SNR is always reported with a context attached.
The European space standards body ECSS defines SNR as the ratio of desired-signal power to coexistent-noise power at a specified point in a transmission channel, under specified conditions. It treats SNR as a measure of signal quality. The point in the channel matters: the same link can show different SNR values at the transmitter, after an amplifier, or at the receiver, because noise is added along the way.
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How the decibel form is calculated
Engineers usually express SNR in decibels (dB). For a power ratio, the formula is:
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SNR (dB) = 10 × log10(signal power ÷ noise power)
The logarithm compresses very large and very small ratios into manageable numbers. The table below shows the values that follow directly from the formula. These are arithmetic conversions, not measurements, and IEEE’s engineering overview on signal-to-noise ratio uses the same mathematical examples.
| Signal-to-noise power ratio | SNR in dB | What it means |
|---|---|---|
| 1 : 1 | 0 dB | Signal and noise have equal power |
| 10 : 1 | 10 dB | Signal power is 10 times noise power |
| 100 : 1 | 20 dB | Signal power is 100 times noise power |
| 1 : 10 | −10 dB | Noise power is 10 times signal power |
Notice that each additional 10 dB represents a tenfold change in power, not a tenfold change in the reading you see on a voltage meter. That leads to the most common source of confusion.
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Amplitude measurements and dB
Voltage, current, sound pressure and similar quantities are amplitudes. Power depends on the square of amplitude, so the decibel conversion for an amplitude ratio is different from the power form. When both signal and noise are measured as amplitudes under the same conditions (for example, across the same impedance), the amplitude form is commonly written as 20 × log10(signal amplitude ÷ noise amplitude). A 10:1 voltage ratio then gives 20 dB, which matches a 100:1 power ratio.
The conversion depends on the quantities and conditions used, so do not assume it. A value written in dB without a note about whether it came from power, mean-square voltage or amplitude cannot be checked against another value.
Definitions change by field
The term has a common core but is not defined identically everywhere. Four authoritative sources show the range.
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Space and telecommunications standards (ECSS)
The ECSS glossary entry on signal-to-noise ratio is the most specific of the sources reviewed. It ties SNR to a named measurement point and to specified conditions, which is what makes a value in a link budget or channel specification meaningful.
Acoustics (Acoustical Society of America)
The Acoustical Society of America (ASA) defines SNR more broadly, as the ratio of a signal measure to the same measure of noise. The measure can be electric power, mean-square voltage or current, or an acoustic analogue. The ASA glossary entry asks that the frequency range and statistical properties of both signal and noise be stated explicitly.
The ASA also points out a practical limit. In many natural conditions, you can only measure signal-plus-noise and noise-alone separately, and the signal alone is then derived rather than measured directly. A reported SNR in acoustics therefore often depends on an estimate, and the estimation method should be given with the number.
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Statistics (NIST Dataplot)
NIST’s Dataplot documentation uses SNR in a different sense. Its Signal to Noise Ratio page defines sample SNR as the sample mean divided by the sample standard deviation, which is the reciprocal of the coefficient of variation. It notes that this definition should typically be used only for ratio-scale data with a meaningful zero. This is a statistical description of data spread, not a measurement of a signal in noise, and it should not be swapped with the power-ratio definition.
Speech in noise (NIST)
NIST’s speech signal-to-noise ratio measurements describe an application-specific estimation method that models the observed signal and noise. Speech SNR values produced by this method should be compared only with values produced by a comparable method.
What to check before comparing two SNR values
Two SNR numbers that look alike can describe very different things. Before deciding that one system is better than another, confirm the following:
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- What is signal and what is noise. A tone, a voice, a data symbol or a background hiss may each be called “signal” in different reports.
- The quantity used. Power, mean-square voltage, amplitude, or a statistical estimator such as the NIST mean-to-standard-deviation form each produce different numbers.
- Frequency range or bandwidth, and any weighting or filtering. Widening the band admits more noise, so the same hardware can report a lower SNR.
- Measurement point and operating conditions. Temperature, load, input level and the position in the chain all change the result.
- How noise was obtained. Whether noise was measured alone or derived from signal-plus-noise changes how much trust the figure deserves.
A bare dB number that does not answer these five points may not support a fair comparison.
Is there a good SNR value?
There is no universal threshold that separates good from poor. The useful value depends on the system, the measurement convention, the bandwidth and the task. A speech recording that is intelligible at one SNR may be unusable for automated analysis at the same level, and a radio link that works with a modest margin in one standard may need more in another. The question to ask is whether the SNR at the stated point, in the stated band, meets the requirement for the specific job. For that requirement, consult the standard or specification that governs your system.
Summary of the definition
SNR compares a desired signal with coexisting noise, usually as a power ratio expressed in decibels. Its meaning is fixed only by the context around it: the definition used, the quantity measured, the band, the point in the system and the conditions. Use the numeric value as a comparison only when those details match.
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