Symbol (data)

In digital communications, symbol rate, also known as baud rate and modulation rate, is the number of symbol changes, waveform changes, or signaling events, across the transmission medium per time unit using a digitally modulated signal or a line code. The symbol rate is measured in baud (Bd) or symbols per second. In the case of a line code, the symbol rate is the pulse rate in pulses per second. Each symbol can represent or convey one or several bits of data. The symbol rate is related to the gross bitrate expressed in bits per second.

A symbol may be described as either a pulse in digital baseband transmission or a tone in passband transmission using modems, representing an integer number of bits. A theoretical definition of a symbol is a waveform, a state or a significant condition of the communication channel that persists for a fixed period of time. A sending device places symbols on the channel at a fixed and known symbol rate, and the receiving device has the job of detecting the sequence of symbols in order to reconstruct the transmitted data. There may be a direct correspondence between a symbol and a small unit of data. For example, each symbol may encode one or several binary digits or 'bits'. The data may also be represented by the transitions between symbols, or even by a sequence of many symbols.

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 T_s can be calculated as:

where f_s is the symbol rate.

The term baud rate has sometimes incorrectly been used to mean bit rate, 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 binary digit (a binary digit always represents one of exactly two states). For this reason, the baud rate value will often be lower than the gross bit rate.

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