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Fig 1: Typical example of Nyquist frequency and rate. They are rarely equal, because that would require over-sampling by a factor of 2 (i.e. 4 times the bandwidth). In signal processing , the Nyquist rate , named after Harry Nyquist , is a value equal to twice the highest frequency ( bandwidth ) of a given function or signal.
The sampling theorem was implied by the work of Harry Nyquist in 1928, [11] in which he showed that up to independent pulse samples could be sent through a system of bandwidth ; but he did not explicitly consider the problem of sampling and reconstruction of continuous signals.
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.
Harry Nyquist's 1924 paper, Certain Factors Affecting Telegraph Speed, contains a theoretical section quantifying "intelligence" and the "line speed" at which it can be transmitted by a communication system, giving the relation W = K log m (recalling the Boltzmann constant), where W is the speed of transmission of intelligence, m is the number ...
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. [A] A sampler is a subsystem or operation that extracts samples from a continuous signal.
The Rayleigh bandwidth of a simple radar pulse is defined as the inverse of its duration. For example, a one-microsecond pulse has a Rayleigh bandwidth of one megahertz. [1] The essential bandwidth is defined as the portion of a signal spectrum in the frequency domain which contains most of the energy of the signal. [2]
Two prominent differences in performance between the two methods are the bandwidth and the signal-to-noise ratio (S/N ratio). The bandwidth of the digital system is determined, according to the Nyquist frequency, by the sample rate used. The bandwidth of an analog system is dependent on the physical and electronic capabilities of the analog ...
In particular, Nyquist determined that the number of independent pulses that could be put through a telegraph channel per unit time is limited to twice the bandwidth of the channel, and published his results in the papers Certain factors affecting telegraph speed (1924) [6] and Certain topics in Telegraph Transmission Theory (1928). [7]