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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 ...
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 of symbol rate, which is one of the components that determine the speed of communication over a data channel. 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 informat ...
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 modulat ...
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 ...
. 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 ...
'', which can be expressed in bits per second. 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, 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. 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 Union ...
) 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 sy ...
, 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: : 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 modulating one or more c ...
, 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 ...
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, als ...
, 1 Bd = 1 bit/s. By contrast, non-digital (or 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 pr ...
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 ...
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 ...
, 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 modulating one or more c ...
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 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 ...
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, Pl ...
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 ...
''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 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 coding, the bit rate is of the baud rate. (A typical basic rate interface 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 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 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 E ...
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