# Baud

In telecommunication and electronics, baud (, unit symbol "Bd") is synonymous to symbols per second or pulses per second. It is the unit of symbol rate, also known as baud or modulation rate; the number of distinct symbol changes (signaling events) made to the transmission medium per second in a digitally modulated signal or a line code. Baud is related to but should not be confused with gross bit rate expressed as bits per second, bps, b/s, bit/s or bits/s. However, though technically incorrect, in the case of modem manufacturers baud commonly refers to bits per second. They make a distinction by also using the term characters per second (CPS). In these anomalous cases, refer to the modem manufacturers documentation to ensure an understanding of their use of the term "baud". An example would be the 1996 User's guide for the U.S. Robotics Sportster modem, which includes these 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:

$T_s = {1 \over f_s},$

where fs is the symbol rate. There is also a chance of miscommunication which leads to ambiguity.

A simple 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.

## Relationship to gross bit rate

The symbol rate is related to but should not be confused with gross bit rate expressed in bit/s. The term baud has sometimes incorrectly been used to mean bit rate,[citation needed] 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 exactly 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:

$f_s = {R \over N}.$

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=6 times the baud. In a line code, these may be M different voltage levels.

The ratio might not even be 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 kbaud.) On the other hand, Manchester coding has a bit rate equal to 1/2 the baud.

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[1] constructed a measure of the gross bitrate R as:

$R = f_s \log_2(M). \,$