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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-T]]) 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''s can be calculated as:

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

where ''f''s is the symbol rate.
There is also a chance of miscommunication, which leads to ambiguity.

: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 ''{{sfrac|1|1000}} second'' (that is, ''1 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 {{nowrap|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''s}} 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''N''}} different symbols are used. In a modem, these may be time-limited [[sine wave]] tones with unique combinations of amplitude, phase or frequency. For example, in a [[64QAM]] modem, {{math|1=''M'' = 64}}, and so the bit rate is {{math|1=''N'' = log2(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 {{nowrap|160 kbit/s}} raw data rate operates at 120 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 symbol 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 |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]]

Baud - Revision history

RS-485: Imported from Wikipedia (overwrite)