Signal-to-noise ratio

Signal-to-noise ratio (SNR, S/NR or S/N) is idea with roots in cybernetics and information theory. It is extensively used in electronic engineering, but has found applications in other fields, such as encoding errors in genetic material. SNR has even entered popular culture, when the particularly incoherent speech of a politician or generic celebrity is described as having an extremely low signal to noise ratio.

SNR is high when the totality of received information is mostly of interest, but is low when much of the received signal is extraneous.

Noise as an abstraction
In this context, noise is any signal, in a channel between sender and receiver, that is not part of the useful content that the receiver desires to hear from the sender.

Improving signal-to-noise ratio
There are several ways to improve the generic SNR:
 * Forward error correction by the transmitter
 * Reducing sources of noise in the systems that prepare the signal of interest for transmission, such as making a microphone more directional
 * Reducing errors in the creation of the signal, such as quantizing distortion in digitizing voice
 * Sending over a communications medium less susceptible to noise (e.g., balanced electrical signals are more noise-immune than unbalanced ones, but sending light over optical fiber is far more noise-immune than electrical transmission)
 * Protecting the communications medium (e.g., shielded wire or coaxial cable)
 * Using multiple communications channels and extracting the common elements (e.g., om radar, pulse trains are the first of many techniques in removing noise in radar systems)
 * Reducing noise entering the receiver (e.g., directional receiving antennas, shielding the receiver chassis)
 * Reducing noise in the reception process (e.g., cooling a receiver component susceptible to thermal noise)

In spectroscopic methods, the S/N ratio can be increased by multiple acquisitions of data because while noise is random, the signal of interest is not. Thus, if a signal is recorded and summed $$n$$ times, the signal intensity increases $$n$$-fold, while the noise increases by $$n^{1/2}$$, leading to a S/N improvement of $$n^{1/2}$$. A much larger increase can be obtained by cooling the electronic components to near liquid helium temperatures, which greatly decreases electronic noise.

Signal-to-noise in specific fields
Do note that a living receiver may be able to improve the effective SNR by the brain's ability to recognize patterns and suppress noise. In telephony, for example, the mean opinion score is a technique of surveying the quality of voice messages as perceived by human listeners with normal hearing.

Audio
An online calculator page, with derivations, discusses Johnson noise, Nyquist noise, and white noise.

Digital imaging
There are specialized techniques for improving SNR in imaging.