In telecommunications and electronics, baud (pronounced /ˈbɔːd/, unit symbol "Bd") is synonymous to symbols per second or pulses per second. It is the unit of symbol rate, also known as baud rate or modulation rate; the number of distinct symbol changes (signaling events) made to the transmission medium per second in a digitally modulated signal or a line code. The baud rate is related to but should not be confused with gross bit rate expressed in bit/s.
The symbol duration time, also known as unit interval, can be directly measured as the time between transitions by looking into an eye diagram of an oscilloscope. The symbol duration time T_{s} can be calculated as:
where f_{s} is the symbol rate.
The baud unit is named after Emile Baudot, the inventor of the Baudot code for telegraphy, and is represented as 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.
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Relationship to gross bit rate
The symbol rate is related to but should not be confused with gross bit rate expressed in bit/s.
The term baud rate has sometimes incorrectly been used to mean bit rate, since these rates are the same in old modems as well as in the simplest digital communication links using only one bit per symbol, such that binary "0" is represented by one symbol, and binary "1" by another symbol. In more advanced modems and data transmission techniques, a symbol may have more than two states, so it may represent more than one bit (a bit (binary digit) always represents one of exactly two states).
If N bits are conveyed per symbol, and the gross bit rate is R, inclusive of channel coding overhead, the symbol rate can be calculated as:
In that case M=2^{N} different symbols are used. In a modem, these may be sinewave tones with unique combinations of amplitude, phase and/or frequency. For example, in a 64QAM modem, M=64, and so the bit rate is N=6 times the baud rate. In a line code, these may be M different voltage levels.
The ratio might not even be an integer; in 4B3T coding, the bit rate is 4/3 the baud rate. (A typical basic rate interface with a 160 kbit/s raw data rate operates at 120 kbaud.) On the other hand, Manchester coding has a bit rate equal to 1/2 the baud rate.
By taking information per pulse N in bit/pulse to be the base2logarithm of the number of distinct messages M that could be sent, Hartley^{[1]} constructed a measure of the gross bitrate R as:
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