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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 that context it is an upper bound for the symbol rate across a bandwidth-limited baseband channel such as a telegraph line [ 2 ] or passband channel such as a limited radio frequency band ...
Nyquist rate: sampling rate twice the bandwidth of the signal's waveform being sampled; sampling at a rate that is equal to, or faster, than this rate ensures that the waveform can be reconstructed accurately. Nyquist frequency: half the sample rate of a system; signal frequencies below this value are unambiguously represented. Nyquist filter
This result was presented by Claude Shannon in 1948 and was based in part on earlier work and ideas of Harry Nyquist and Ralph Hartley. The Shannon limit or Shannon capacity of a communication channel refers to the maximum rate of error-free data that can theoretically be transferred over the channel if the link is subject to random data ...
The term Nyquist Sampling Theorem (capitalized thus) appeared as early as 1959 in a book from his former employer, Bell Labs, [22] and appeared again in 1963, [23] and not capitalized in 1965. [24] It had been called the Shannon Sampling Theorem as early as 1954, [ 25 ] but also just the sampling theorem by several other books in the early 1950s.
Some of the oldest methods of telecommunications implicitly use many of the ideas that would later be quantified in information theory. Modern telegraphy, starting in the 1830s, used Morse code, in which more common letters (like "E", which is expressed as one "dot") are transmitted more quickly than less common letters (like "J", which is expressed by one "dot" followed by three "dashes").
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.
where is the pulse frequency (in pulses per second) and is the bandwidth (in hertz). The quantity later came to be called the Nyquist rate, and transmitting at the limiting pulse rate of pulses per second as signalling at the Nyquist rate. Nyquist published his results in 1928 as part of his paper "Certain topics in Telegraph Transmission Theory".
The field was established and put on a firm footing by Claude Shannon in the 1940s, [1] though early contributions were made in the 1920s through the works of Harry Nyquist and Ralph Hartley. It is at the intersection of electronic engineering, mathematics, statistics, computer science, neurobiology, physics, and electrical engineering. [2] [3]