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Early uses of the term Nyquist frequency, such as those cited above, are all consistent with the definition presented in this article.Some later publications, including some respectable textbooks, call twice the signal bandwidth the Nyquist frequency; [6] [7] this is a distinctly minority usage, and the frequency at twice the signal bandwidth is otherwise commonly referred to as the Nyquist rate.
The Nyquist–Shannon sampling theorem is an essential principle for digital signal processing linking the frequency range of a signal and the sample rate required to avoid a type of distortion called aliasing. The theorem states that the sample rate must be at least twice the bandwidth of the signal to avoid aliasing.
Note that the Nyquist rate is a property of a continuous-time signal, whereas Nyquist frequency is a property of a discrete-time system. The term Nyquist rate is also used in a different context with units of symbols per second, which is actually the field in which Harry Nyquist was working.
In signal processing, sampling is the reduction of a continuous-time signal to a discrete-time signal. A common example is the conversion of a sound wave to a sequence of "samples". A sample is a value of the signal at a point in time and/or space; this definition differs from the term's usage in statistics , which refers to a set of such values.
In information theory, a signal is a codified message, that is, the sequence of states in a communication channel that encodes a message. In a communication system, a transmitter encodes a message to create a signal, which is carried to a receiver by the communication channel.
To derive the criterion, we first express the received signal in terms of the transmitted symbol and the channel response. Let the function h(t) be the channel impulse response, x[n] the symbols to be sent, with a symbol period of T s; the received signal y(t) will be in the form (where noise has been ignored for simplicity):
Since each tone (i.e., symbol) represents a message consisting of two digital bits in this example, the bit rate is twice the symbol rate, i.e. 2000 bits per second. According to one definition of digital signal, [3] the modulated signal is a digital signal. According to another definition, the modulation is a form of digital-to-analog conversion.
A signaling protocol is a type of communications protocol for encapsulating the signaling between communication endpoints and switching systems to establish or terminate a connection and to identify the state of connection. The following is a list of signaling protocols: ALOHA; Digital Subscriber System No. 1 (EDSS1) Dual-tone multi-frequency ...