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{{Short description|Symbol rate measurement in telecommunications}}
{{other uses}}

In [[telecommunications]] and [[electronics]], '''baud''' ({{IPAc-en|b|ɔː|d}}; symbol: '''Bd''') is a common [[unit of measurement]] of [[symbol rate]], which is one of the components that determine the [[Speed of service|speed of communication]] over a [[data channel]].

It is the unit for symbol rate or [[modulation]] rate in '''symbols per second''' or '''pulses per second'''. It is the number of distinct [[symbol (data)|symbol]] changes (signalling events) made to the [[transmission medium]] per second in a digitally modulated signal or a bd rate [[line code]].

Baud is related to ''[[gross bit rate]]'', which can be expressed in [[bits per second]] (bit/s).<ref>{{Cite news|url=http://www.electronicdesign.com/communications/what-s-difference-between-bit-rate-and-baud-rate|title=What's The Difference Between Bit Rate And Baud Rate?|date=2012-04-27|work=Electronic Design|access-date=2018-01-18}}</ref> If there are precisely two symbols in the system (typically 0 and 1), then baud and bits per second are equivalent.

== Naming ==
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 [[ITU]]) in November 1926. The earlier standard had been the number of words per minute, which was a less robust measure since word length can vary.<ref>{{Cite web|url=http://www.linfo.org/baud.html|title=Baud definition by The Linux Information Project (LINFO)|website=www.linfo.org|access-date=2018-01-18}}</ref>

==Definitions==
The symbol duration time, also known as the [[unit interval (data transmission)|unit interval]], can be directly measured as the time between transitions by looking at an [[eye diagram]] of the signal on an [[oscilloscope]]. The symbol duration time ''T''<sub>s</sub> can be calculated as:

:<math> T_\text{s}  =  {1 \over f_\text{s}}, </math>

where ''f''<sub>s</sub> is the symbol rate.
There is also a chance of miscommunication which leads to ambiguity.

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

The baud is scaled using standard [[metric prefix]]es, 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 [[gross bit rate]] expressed in bit/s.
The term baud has sometimes incorrectly been used to mean [[bit rate]],<ref>{{cite web |url=http://www.textfiles.com/apple/bitsbaud.txt |title=BITS, BAUD RATE, AND BPS Taking the Mystery Out of Modem Speeds |last1=Banks |first1=Michael A. |date=1990 |publisher=Brady Books/Simon & Schuster |access-date=17 September 2014}}</ref> since these rates are the same in old [[modem]]s as well as in the simplest digital communication links using only one bit per symbol, such that binary digit "0" is represented by one symbol, and binary digit "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 two states.

If {{mvar|N}} bits are conveyed per symbol, and the gross bit rate is {{mvar|R}}, inclusive of channel coding overhead, the symbol rate {{math|''f''<sub>s</sub>}} can be calculated as

:<math>  f_\text{s}  =   {R \over N}. </math>

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, [[Ralph Hartley|Hartley]]<ref>{{cite book | title = Information Theory and its Engineering Applications | author = D. A. Bell | edition = 3rd | year = 1962 | publisher = Pitman | location = New York |oclc=1626214}}</ref> constructed a measure of the [[gross bit rate]] ''R'' as

:<math>  R  =   f_\text{s} N\quad  </math>  where <math>\quad N = \left \lceil \log_2(M) \right \rceil.</math>

Here, the <math>\left \lceil x \right \rceil</math> denotes the ceiling function of <math>x</math>, where <math>x</math> is taken to be any real number greater than zero, then the ceiling function rounds up to the nearest natural number (e.g. <math>\left \lceil 2.11 \right \rceil = 3</math>).

In that case, {{math|1=''M'' = 2<sup>''N''</sup>}} 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 [[64QAM]] modem, {{math|1=''M'' = 64}}, and so the bit rate is {{math|1=''N'' = log<sub>2</sub>(64) = 6}} times the baud rate. In a line code, these may be ''M'' different voltage levels.

The ratio is not necessarily an integer; in [[4B3T]] coding, the bit rate is {{sfrac|4|3}} of the baud rate.  (A typical [[basic rate interface]] with a 160&nbsp;kbit/s raw data rate operates at 120&nbsp;kBd.) 

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 (computing)|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 {{sfrac|8|17}}{{efn|EFM requires three merging bits between adjacent fourteen-bit codewords.}} of the baud rate.

==See also==
{{columns-list|colwidth=20em|
* [[Serial_port#Settings|Commonly used baud rates]]
* [[Constellation diagram]]
* [[List of device bandwidths]]
* [[Mark and space]]
* [[Nyquist rate]]
* [[Pulse-code modulation]]
}}

==Notes==
{{Notelist}}

==References==
{{Reflist}}

==External links==
* {{cite journal
| title=On the origins of serial communications and data encoding
| url=http://www.dbase.com/Knowledgebase/dbulletin/bu07sh.htm
| first=Nicolas | last=Martin
| journal=dBulletin, the dBASE Developers Bulletin<!--Citation bot --> |issue=7 |date=January 2000
| access-date=January 4, 2007
}}
* {{cite journal |title=What's The Difference Between Bit Rate And baud?
| first=Lou | last=Frenzel
| journal=Electronic Design Magazine |date=April 27, 2012
| url=http://electronicdesign.com/communications/what-s-difference-between-bit-rate-and-baud-rate
}}
[[Category:Data transmission]]
[[Category:Units of frequency]]