Editing Shannon–Hartley theorem (section)

==Statement of the theorem==

The Shannon–Hartley theorem states the [[channel capacity]] <math>C</math>, meaning the theoretical [[Tightness of measures|tightest]] upper bound on the [[information rate]] of data that can be communicated at an arbitrarily low [[bit error rate|error rate]] using an average received signal power <math>S</math> through an analog communication channel subject to [[additive white Gaussian noise]] (AWGN) of power {{nowrap|<math>N</math>:}}

:<math>C = B \log_2 \left( 1+\frac{S}{N} \right) </math>

where
* <math>C</math> is the [[channel capacity]] in [[bits per second]], a theoretical upper bound on the [[net bit rate]] (information rate, sometimes denoted <math>I</math>) excluding error-correction codes;
* <math>B</math> is the [[bandwidth (signal processing)|bandwidth]] of the channel in [[hertz]] ([[passband]] bandwidth in case of a bandpass signal);
* <math>S</math> is the average received signal power over the bandwidth (in case of a carrier-modulated passband transmission, often denoted ''[[Carrier-to-noise ratio|C]]''), measured in watts (or volts squared);
* <math>N</math> is the average power of the noise and interference over the bandwidth, measured in watts (or volts squared); and
* <math>S/N</math> is the [[signal-to-noise ratio]] (SNR) or the [[carrier-to-noise ratio]] (CNR) of the communication signal to the noise and interference at the receiver (expressed as a linear power ratio, not as logarithmic [[decibels]]).