Often written as

S/N ratio or SNR, and is basically a measure of signal strength

relative to

background noise, used principally in

communications.

Mathematically it is expressed:

SNR=SIGNAL POWER
------------
NOISE POWER

or in

dB

SNRdb=10log10(SIGNAL POWER)
(------------)
(NOISE POWER )

Often the powers involved are not known, but the

voltage amplitude is. In this case it is possible to substitute V

^{2}/R for P. This gives us the much more common:

SNR=20log10(V1)
(--)dB
(V2)

Hence, if the

power of the noise is equal to the power of the signal the SNR would be

zero and the information would be almost unreadable. In communications, this would be mean the information would often have to be sent again since there would be frequent errors. A low SNR would therefore mean a slow transfer of information, so is something that is not desired.

SNR is practically used in many applications, for instance the Shannon-Hartley Law of communication. It is a large factor for powerful telescopes, where errors can provide wildly wrong information.

Typically accepted SNR would be 20dB in telegraphy and in 30dB in cable TV.