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In
telecommunication Telecommunication is the transmission of information by various types of technologies over wire, radio, optical, or other electromagnetic systems. It has its origin in the desire of humans for communication over a distance greater than that fe ...
and
electronics The field of electronics is a branch of physics and electrical engineering that deals with the emission, behaviour and effects of electrons using electronic devices. Electronics uses active devices to control electron flow by amplification ...
, baud (; symbol: Bd) is a common
unit of measurement A unit of measurement is a definite magnitude (mathematics), magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity. Any other quantity of that kind can ...
of
symbol rate In a digitally modulated signal or a line code, symbol rate, modulation rate or baud rate is the number of symbol changes, waveform changes, or signaling events across the transmission medium per unit of time. The symbol rate is measured in ''b ...
, which is one of the components that determine the speed of communication over a
data channel A communication channel refers either to a physical transmission medium such as a wire, or to a logical connection over a multiplexed medium such as a radio channel in telecommunications and computer networking. A channel is used for informat ...
. It is the unit for symbol rate or
modulation In electronics and telecommunications, modulation is the process of varying one or more properties of a periodic waveform, called the ''carrier signal'', with a separate signal called the ''modulation signal'' that typically contains informatio ...
rate in symbols per second or pulses per second. It is the number of distinct
symbol A symbol is a mark, sign, or word that indicates, signifies, or is understood as representing an idea, object, or relationship. Symbols allow people to go beyond what is known or seen by creating linkages between otherwise very different conc ...
changes (signalling events) made to the
transmission medium A transmission medium is a system or substance that can mediate the propagation of signals for the purposes of telecommunication. Signals are typically imposed on a wave of some kind suitable for the chosen medium. For example, data can modulate ...
per second in a digitally modulated signal or a bd rate
line code In telecommunication, a line code is a pattern of voltage, current, or photons used to represent digital data transmitted down a communication channel or written to a storage medium. This repertoire of signals is usually called a constrained c ...
. Baud is related to ''
gross bit rate In telecommunications and computing, bit rate (bitrate or as a variable ''R'') is the number of bits that are conveyed or processed per unit of time. The bit rate is expressed in the unit bit per second (symbol: bit/s), often in conjunction w ...
'', which can be expressed in
bits per second In telecommunications and computing, bit rate (bitrate or as a variable ''R'') is the number of bits that are conveyed or processed per unit of time. The bit rate is expressed in the unit bit per second (symbol: bit/s), often in conjunction w ...
. If there are precisely two symbols in the system (typically 0 and 1), then baud and bit per second (bit/s) are equivalent.


Naming

The baud unit is named after
Émile Baudot Jean-Maurice-Émile Baudot (; 11 September 1845 – 28 March 1903), French telegraph engineer and inventor of the first means of digital communication Baudot code, was one of the pioneers of telecommunications. He invented a multiplexed printi ...
, the inventor of the
Baudot code The Baudot code is an early character encoding for telegraphy invented by Émile Baudot in the 1870s. It was the predecessor to the International Telegraph Alphabet No. 2 (ITA2), the most common teleprinter code in use until the advent of ASCII. ...
for
telegraphy Telegraphy is the long-distance transmission of messages where the sender uses symbolic codes, known to the recipient, rather than a physical exchange of an object bearing the message. Thus flag semaphore is a method of telegraphy, whereas p ...
, and is represented according to the rules for
SI units The International System of Units, known by the international abbreviation SI in all languages and sometimes Pleonasm#Acronyms and initialisms, pleonastically as the SI system, is the modern form of the metric system and the world's most wid ...
. 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. It was defined by the CCITT (now the
ITU The International Telecommunication Union is a specialized agency of the United Nations responsible for many matters related to information and communication technologies. It was established on 17 May 1865 as the International Telegraph Unio ...
) 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.


Definitions

The
symbol duration time The unit interval is the minimum time interval between condition changes of a data transmission signal, also known as the pulse time or symbol duration time. A unit interval (UI) is the time taken in a data stream by each subsequent pulse (or s ...
, can be directly measured as the time between transitions by looking at an
eye diagram In telecommunication, an eye pattern, also known as an eye diagram, is an oscilloscope display in which a digital signal from a receiver is repetitively sampled and applied to the vertical input, while the data rate is used to trigger the horizon ...
of the signal on an
oscilloscope An oscilloscope (informally a scope) is a type of electronic test instrument that graphically displays varying electrical voltages as a two-dimensional plot of one or more signals as a function of time. The main purposes are to display repetiti ...
. The symbol duration time ''T''s can be calculated as: : T_\text = , 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 A modulator-demodulator or modem is a computer hardware device that converts data from a digital format into a format suitable for an analog transmission medium such as telephone or radio. A modem transmits data by Modulation#Digital modulati ...
, 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 '' second'' (that is, ''1 millisecond''). In
digital Digital usually refers to something using discrete digits, often binary digits. Technology and computing Hardware *Digital electronics, electronic circuits which operate using digital signals **Digital camera, which captures and stores digital i ...
systems (i.e., using discrete/discontinuous values) with
binary code A binary code represents text, computer processor instructions, or any other data using a two-symbol system. The two-symbol system used is often "0" and "1" from the binary number system. The binary code assigns a pattern of binary digits, also ...
, 1 Bd = 1 bit/s. By contrast, non-digital (or
analog Analog or analogue may refer to: Computing and electronics * Analog signal, in which information is encoded in a continuous variable ** Analog device, an apparatus that operates on analog signals *** Analog electronics, circuits which use analog ...
) systems use a continuous range of values to represent information and in these systems the exact informational size of 1 Bd varies. The baud is scaled using standard
metric prefix A metric prefix is a unit prefix that precedes a basic unit of measure to indicate a multiple or submultiple of the unit. All metric prefixes used today are decadic. Each prefix has a unique symbol that is prepended to any unit symbol. The pre ...
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 In telecommunications and computing, bit rate (bitrate or as a variable ''R'') is the number of bits that are conveyed or processed per unit of time. The bit rate is expressed in the unit bit per second (symbol: bit/s), often in conjunction w ...
expressed in bit/s. The term baud has sometimes incorrectly been used to mean
bit rate In telecommunications and computing, bit rate (bitrate or as a variable ''R'') is the number of bits that are conveyed or processed per unit of time. The bit rate is expressed in the unit bit per second (symbol: bit/s), often in conjunction w ...
, since these rates are the same in old
modem A modulator-demodulator or modem is a computer hardware device that converts data from a digital format into a format suitable for an analog transmission medium such as telephone or radio. A modem transmits data by Modulation#Digital modulati ...
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 The bit is the most basic unit of information in computing and digital communications. The name is a portmanteau of binary digit. The bit represents a logical state with one of two possible values. These values are most commonly represente ...
. A bit (binary digit) always represents one of two states. If bits are conveyed per symbol, and the gross bit rate is , inclusive of channel coding overhead, the symbol rate can be calculated as : f_\text = . By taking information per pulse ''N'' in bit/pulse to be the base-2-
logarithm In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a number  to the base  is the exponent to which must be raised, to produce . For example, since , the ''logarithm base'' 10 o ...
of the number of distinct messages ''M'' that could be sent,
Hartley Hartley may refer to: Places Australia *Hartley, New South Wales *Hartley, South Australia **Electoral district of Hartley, a state electoral district Canada *Hartley Bay, British Columbia United Kingdom *Hartley, Cumbria *Hartley, Plymou ...
constructed a measure of the
gross bit rate In telecommunications and computing, bit rate (bitrate or as a variable ''R'') is the number of bits that are conveyed or processed per unit of time. The bit rate is expressed in the unit bit per second (symbol: bit/s), often in conjunction w ...
''R'' as : R = f_\text N\quad where \quad N = \left \lceil \log_2(M) \right \rceil. Here, the \left \lceil x \right \rceil denotes the ceiling function of x. Where x is taken to be any real number greater than zero, then the ceiling function rounds up to the nearest natural number (e.g. \left \lceil 2.11 \right \rceil = 3). In that case, 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 Quadrature amplitude modulation (QAM) is the name of a family of digital modulation methods and a related family of analog modulation methods widely used in modern telecommunications to transmit information. It conveys two analog message signal ...
modem, , and so the bit rate is times the baud rate. In a line code, these may be ''M'' different voltage levels. The ratio is not necessarily even an integer; in
4B3T 4B3T, which stands for 4 (four) binary 3 (three) ternary, is a line encoding scheme used for ISDN PRI interface. 4B3T represents four binary bits using three pulses. Description It uses three states: * + (positive pulse), * 0 (no pulse), and * â ...
coding, the bit rate is of the baud rate. (A typical
basic rate interface Basic Rate Interface (BRI, 2B+D, 2B1D) or Basic Rate Access is an Integrated Services Digital Network (ISDN) configuration intended primarily for use in subscriber lines similar to those that have long been used for voice-grade telephone service ...
with a 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 Bandwidth commonly refers to: * Bandwidth (signal processing) or ''analog bandwidth'', ''frequency bandwidth'', or ''radio bandwidth'', a measure of the width of a frequency range * Bandwidth (computing), the rate of data transfer, bit rate or thr ...
but a high
signal-to-noise ratio Signal-to-noise ratio (SNR or S/N) is a measure used in science and engineering that compares the level of a desired signal to the level of background noise. SNR is defined as the ratio of signal power to the noise power, often expressed in deci ...
within that bandwidth. In other applications, the bit rate is less than the symbol rate.
Eight-to-fourteen modulation Eight-to-fourteen modulation (EFM) is a data encoding technique – formally, a ''line code'' – used by compact discs (CD), laserdiscs (LD) and pre-Hi-MD MiniDiscs. EFMPlus is a related code, used in DVDs and Super Audio CDs (SACDs). EFM and ...
as used on audio CDs has bit rate of the baud rate.


See also


References


External links

* * {{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 Data transmission Units of frequency