Signal-to-noise ratio

A ratio higher than 1:1 (greater than 0 dB) indicates more signal than noise.

A high SNR means that the signal is clear and easy to detect or interpret, while a low SNR means that the signal is corrupted or obscured by noise and may be difficult to distinguish or recover.

SNR can be calculated using different formulas depending on how the signal and noise are measured and defined.

The most common way to express SNR is in decibels, which is a logarithmic scale that makes it easier to compare large or small values.

Other definitions of SNR may use different factors or bases for the logarithm, depending on the context and application.

If the noise has expected value of zero, as is common, the denominator is its variance, the square of its standard deviation σN.

However, when the signal and noise are measured in volts (V) or amperes (A), which are measures of amplitude,[note 1] they must first be squared to obtain a quantity proportional to power, as shown below: The concepts of signal-to-noise ratio and dynamic range are closely related.

Measuring signal-to-noise ratios requires the selection of a representative or reference signal.

In audio engineering, the reference signal is usually a sine wave at a standardized nominal or alignment level, such as 1 kHz at +4 dBu (1.228 VRMS).

The concept can be understood as normalizing the noise level to 1 (0 dB) and measuring how far the signal 'stands out'.

This may cause some confusion among readers, but the resistance factor is not significant for typical operations performed in signal processing, or for computing power ratios.

[note 2] Notice that such an alternative definition is only useful for variables that are always non-negative (such as photon counts and luminance), and it is only an approximation since

This includes electronic noise, but can also include external events that affect the measured phenomenon — wind, vibrations, the gravitational attraction of the moon, variations of temperature, variations of humidity, etc., depending on what is measured and of the sensitivity of the device.

Internal electronic noise of measurement systems can be reduced through the use of low-noise amplifiers.

For example, a lock-in amplifier can extract a narrow bandwidth signal from broadband noise a million times stronger.

When the signal is constant or periodic and the noise is random, it is possible to enhance the SNR by averaging the measurements.

This theoretical maximum SNR assumes a perfect input signal.

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: 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.

In this case, the SNR is approximately Floating-point numbers provide a way to trade off signal-to-noise ratio for an increase in dynamic range.

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.

To describe the signal quality without taking the receiver into account, the optical SNR (OSNR) is used.

For instance an OSNR of 20 dB/0.1 nm could be given, even the signal of 40 GBit DPSK would not fit in this bandwidth.

The term is sometimes used metaphorically to refer to the ratio of useful information to false or irrelevant data in a conversation or exchange.

[14] SNR can also be applied in marketing and how business professionals manage information overload.

Managing a healthy signal to noise ratio can help business executives improve their KPIs (Key Performance Indicators).

[15] The signal-to-noise ratio is similar to Cohen's d given by the difference of estimated means divided by the standard deviation of the data