# Baud

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In telecommunication and electronics, baud (/bɔːd/; symbol: Bd) is a common measure of symbol rate, one of the components that determine the 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 changes (signaling events) made to the transmission medium per second in a digitally modulated signal or a bd rate line code.

Baud is related to, but not equivalent to, gross bit rate, which can be expressed as bits per second.[1] If there are only two symbols in the system (typically 0 and 1), then baud and bits per second (bps) are equivalent.

## Naming

The baud unit is named after Émile Baudot, the inventor of the Baudot code for telegraphy, and is represented in accordance with 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) in November 1926. The earlier standard had been the number of words per minute. One baud was equal to one pulse per second, a more robust measure as word length can vary.[2]

## Definitions

The symbol duration time, also known as 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 Ts can be calculated as:

${\displaystyle T_{s}={1 \over f_{s}},}$

where fs 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 1/1000 second (that is, 1 millisecond).

In digital systems (i.e., using discrete/discontinuous values) with binary code, 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 prefixes, 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,[3] 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 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 N bits are conveyed per symbol, and the gross bit rate is R, inclusive of channel coding overhead, the symbol rate fs can be calculated as

${\displaystyle f_{\mathrm {s} }={R \over N}.}$

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[4] constructed a measure of the gross bitrate R as

${\displaystyle R=f_{\mathrm {s} }N\quad }$ where ${\displaystyle \quad N=\log _{2}(M).}$

In that case M = 2N, 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, M = 64, and so the bit rate is N = log2(64) = 6 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 4/3 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 as used on audio CDs has bit rate 8/14 of the baud rate.

## References

1. ^ "What's The Difference Between Bit Rate And Baud Rate?". Electronic Design. 2012-04-27. Retrieved 2018-01-18.
2. ^ "Baud definition by The Linux Information Project (LINFO)". www.linfo.org. Retrieved 2018-01-18.
3. ^ Banks, Michael A. (1990). "BITS, BAUD RATE, AND BPS Taking the Mystery Out of Modem Speeds". Brady Books/Simon & Schuster. Retrieved 17 September 2014.
4. ^ D. A. Bell (1962). Information Theory and its Engineering Applications (3rd ed.). New York: Pitman. OCLC 1626214.