Signal-to-noise ratio measures how far a message stands out from the hiss
Every radio broadcast, radar echo, photograph and recording carries some unwanted background along with the part you care about. Engineers boil the contest down to one number, the signal-to-noise ratio. Above zero decibels the signal is winning; below it, the message is sinking into the static, and the ratio even caps how much data a channel can carry.
At heart the measure is simple: the average power of the wanted signal divided by the average power of the noise. Both must be measured at the same point in a system and across the same band of frequencies, or the comparison is meaningless. A useful way to picture it is to set the noise level to one and ask how far above that the signal rises. The figure usually describes an average, since at any given instant the ratio can swing a great deal.
Because real signals span enormous ranges, the ratio is usually quoted on the logarithmic decibel scale, where multiplying ten times the base-ten logarithm of the power ratio gives the answer. That brings a handy shortcut: if signal and noise are already in decibels, just subtract one from the other. Measure voltages or currents rather than power, though, and you must square them first, which turns the factor of ten into twenty. Signal processing texts often drop the resistance term from power calculations entirely, a habit that confuses newcomers but leaves ratios unchanged.
It is easy to mix up with dynamic range. That compares the strongest undistorted signal a channel can handle with the faintest one detectable, whereas signal-to-noise ratio compares any chosen signal level with the noise. Measuring it therefore needs an agreed reference; audio engineers commonly use a 1 kilohertz tone at a standard level of plus 4 dBu.
The stakes reach beyond clarity. According to the Shannon-Hartley theorem, a cornerstone of information theory, a channel's bandwidth and its signal-to-noise ratio together set the most data it can reliably carry. Engineers raise the ratio by boosting the signal, cutting noise at the source, filtering or adding error correction. For always-positive quantities such as photon counts, an alternative version divides the mean by the standard deviation.
Source: Signal-to-noise ratio
