Signal-to-noise ratio (SNR, also written S/N) compares a desired signal with the noise that exists alongside it. In common engineering usage, it is the ratio of signal power to noise power. A higher SNR means the signal stands out more clearly from the noise under the conditions in which it was measured. The number is only meaningful when the report also says what was counted as signal, what was counted as noise, where the measurement was taken, and over which frequency range.
What the term means
SNR is a relative measure, not an absolute strength reading. A signal at 2 volts is neither strong nor weak until you know how much noise accompanies it. The European Cooperation for Space Standardization (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, and treats it as a measure of signal quality. The ECSS signal-to-noise ratio glossary entry sets out those elements explicitly.
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The decibel form and what the numbers mean
For a power ratio, SNR in decibels (dB) is calculated as:
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The IEEE Technology Navigator overview uses the same power-ratio conversion. Some reference values that follow directly from the formula:
| Signal power to noise power | SNR in dB | Reading |
|---|---|---|
| 1 : 10 | −10 dB | Noise power is ten times the signal power |
| 1 : 1 | 0 dB | Signal and noise powers are equal |
| 10 : 1 | 10 dB | Signal power is ten times the noise power |
| 100 : 1 | 20 dB | Signal power is one hundred times the noise power |
| 1,000 : 1 | 30 dB | Signal power is one thousand times the noise power |
These values are arithmetic consequences of the formula, not measurements from any particular system. Each 10 dB step is a tenfold change in power, so a gain from 20 dB to 30 dB means the power ratio went from 100 to 1,000.
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How the definition changes by field
The same term is used in several disciplines with slightly different meanings. Before comparing two figures, identify which definition the author used.
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Telecommunications and space systems
The ECSS definition is built around a point in a transmission channel. The SNR at a receiver input can differ from the SNR at a demodulator output, because processing can change how signal and noise are distributed. The ECSS entry ties the number to that specified point and its conditions.
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Acoustics
The Acoustical Society of America (ASA) glossary defines SNR as a 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 glossary says that the frequency range and statistical properties of the signal and noise should be stated explicitly. It also notes that, under many natural conditions, measurements capture only signal-plus-noise and noise-alone. In those cases the SNR is derived from the two measurements rather than obtained by measuring the signal separately. See the ASA signal-to-noise ratio glossary entry.
Statistical data analysis
NIST’s Dataplot documentation uses SNR in a different sense: the sample mean divided by the sample standard deviation, which is the reciprocal of the coefficient of variation. The documentation says this form should typically be used only for ratio-scale data that has a meaningful zero. It is a statistical estimator, not a substitute for the power ratio used in communications. The NIST Dataplot signal-to-noise ratio reference describes its scope.
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Speech in noise
NIST’s speech measurement work describes an application-specific estimation method that models the observed signal and noise. Speech SNR values therefore depend on the estimation method as well as the recording. For details, see NIST’s speech signal-to-noise ratio measurements page.
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The formula above is for power ratios. Engineers often have voltages, pressures or other amplitudes instead. Converting an amplitude ratio to decibels uses a different multiplier, commonly 20 × log10, but that convention holds only when the amplitudes relate to power through a squared relationship under the same measurement conditions, such as the same impedance. When a report gives a dB value for amplitude quantities, check whether the author applied the power convention or the amplitude convention. Mixing them can change the reported figure by a factor of two in dB terms.
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How to compare two reported SNR values
A raw dB number is not enough to rank two systems. Check these points in order:
- Signal and noise definitions. What did the author count as signal, and what counted as noise? Interference, quantization error and background sound are often treated differently.
- Quantity used. Was the ratio based on power, mean-square voltage or current, amplitude, or a statistical estimator such as mean divided by standard deviation?
- Frequency range or bandwidth. Note any filtering or weighting. A wider bandwidth admits more noise, so a wider-band figure is often lower for the same hardware.
- Measurement point and conditions. Was the value measured at the input, at the output, or after processing? What temperature, level, or operating mode applied?
- How noise was obtained. Was noise measured alone, or derived from signal-plus-noise measurements? Derived values depend on the estimation model.
If any of these five points is missing, treat the number as a label for that specific measurement rather than a basis for comparison.
Is there a good signal-to-noise ratio?
There is no universal threshold. Whether a value is adequate depends on the system, the measurement convention, the bandwidth and the task. A figure that is more than enough for recognising a spoken word over a telephone line may be inadequate for measuring a faint laboratory signal. Set the requirement for your application first, then judge the measured value against it, using the same definition, bandwidth and measurement point.
Key points to remember
- SNR compares a desired signal with coexisting noise; it is not an absolute signal level.
- In the power-ratio form, 0 dB means equal powers, and each 10 dB is a tenfold power ratio.
- Definitions vary by field, including the ECSS channel-point definition, the ASA measure-based definition and NIST’s statistical estimator.
- Amplitude-based dB figures use a different convention from power-based ones.
- Compare SNR values only when signal, noise, bandwidth, measurement point and estimation method match.
The definition is simple, but the number carries meaning only through the conditions that produced it.
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