# Baud

For other uses, see Baud (disambiguation).

In telecommunication and electronics, baud (/ˈbɔːd/, unit symbol Bd) 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 line code.

Digital data modem manufacturers commonly define the baud as the modulation rate of data transmission and express it as bits per second.[1]

Baud is related to gross bit rate expressed as bits per second.

## Definitions

The symbol duration time, also known as unit interval, can be directly measured as the time between transitions by looking into an eye diagram of 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: a baud of 1 kBd = 1,000 Bd is synonymous to a symbol rate of 1,000 symbols per second. In case of a modem, this corresponds to 1,000 tones per second, and in case of a line code, this corresponds to 1,000 pulses per second. The symbol duration time is 1/1,000 second = 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 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.

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,[2] 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 "0" is represented by one symbol, and binary "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[3] 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 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. 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 baud. (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. Manchester coding and modified frequency modulation have a bit rate equal to 1/2 the baud. Eight-to-fourteen modulation as used on audio CDs has bit rate which 8/17 of the baud.

## References

1. ^ AT&T, Bell System Data Communications Technical Reference, Data Set 103F Interface Specification, May 1964
2. ^ Banks, Michael A. (1990). "BITS, BAUD RATE, AND BPS Taking the Mystery Out of Modem Speeds". Brady Books/Simon & Schuster. Retrieved 17 September 2014.
3. ^ D. A. Bell (1962). Information Theory and its Engineering Applications (3rd ed.). New York: Pitman. OCLC 1626214.