Baud

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For the town in France, see Baud, Morbihan.

In telecommunications and electronics, baud (pronounced /ˈbɔːd/, unit symbol "Bd") is synonymous to symbols/s or pulses/s. It is the unit of symbol rate, also known as baud rate or modulation rate; the number of distinct symbol changes (signalling 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 Ts can be calculated as:

T_s = {1 \over f_s},

where fs is the symbol rate.

A simple example: A baud rate of 1 kBd = 1,000 Bd is synonymous to a symbol rate of 1,000 symbols per second. In case of a modem, this corresponds to 1,000 tones per second, and in case of a line code, this corresponds to 1,000 pulses per second. The symbol duration time is 1/1,000 second = 1 millisecond.

The baud unit is named after Emile Baudot, the inventor of the Baudot code for telegraphy, and is represented as SI units are. 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.

[edit] 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 binary bit (a binary bit always represents 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:

f_s = {R \over N}.

In that case M=2N 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. In a line code, these may be M different voltage levels.

By taking information per pulse N in bit/pulse to be the base-2-logarithm of the number of distinct messages M that could be sent, Hartley[1] constructed a measure of the gross bitrate R as:

R = f_s \log_2(M), \,

where fs is the baud rate in symbols/second or pulses/second. (See Hartley's law).

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