Baud

The baud unit is named after Émile Baudot, the inventor of the Baudot code for telegraphy, and is represented according to the rules for SI units. That is, the first letter of its symbol is uppercase (Bd), but when the unit is spelled out, it should be written in lowercase (baud) except when it begins a sentence or is capitalized for another reason, such as in title case. It was defined by the CCITT (now the

Example: Communication at the baud rate 1000 Bd means communication by means of sending 1000 symbols per second. In the case of a modem, this corresponds to 1000 tones per second; similarly, in the case of a line code, this corresponds to 1000 pulses per second. The symbol duration time is 1/1000 second (that is, 1 millisecond).

The baud is scaled using standard metric prefixes, so that for example

• 1 kBd (kilobaud) = 1000 Bd
• 1 MBd (megabaud) = 1000 kBd
• 1 GBd (gigabaud) = 1000 MBd

Relationship to gross bit rate

The symbol rate is related to

If N bits are conveyed per symbol, and the gross bit rate is R, inclusive of channel coding overhead, the symbol rate f_s can be calculated as

${\displaystyle f_{\text{s}}={R \over N}.}$

By taking information per pulse N in bit/pulse to be the base-2-

${\displaystyle R=f_{\text{s}}N\quad }$ where ${\displaystyle \quad N=\left\lceil \log _{2}(M)\right\rceil .}$

Here, the ${\displaystyle \left\lceil x\right\rceil }$ denotes the ceiling function of ${\displaystyle x}$. Where ${\displaystyle x}$ is taken to be any real number greater than zero, then the ceiling function rounds up to the nearest natural number (e.g. ${\displaystyle \left\lceil 2.11\right\rceil =3}$).

In that case, M = 2^N different symbols are used. In a modem, these may be time-limited sinewave tones with unique combinations of amplitude, phase and/or frequency. For example, in a

The ratio is not necessarily an integer; in

Codes with many symbols, and thus a bit rate higher than the symbol rate, are most useful on channels such as telephone lines with a limited bandwidth but a high signal-to-noise ratio within that bandwidth. In other applications, the bit rate is less than the symbol rate. Eight-to-fourteen modulation as used on audio CDs has bit rate 8/17^[a] of the baud rate.

See also

Notes

References