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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.
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 of a given function or signal
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 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]
Writer Alex Bellos described The Mathematics of Life as "a testament to the versatility of maths and how it is shaping our understanding of the world." [4] Kirkus Reviews called the book "an ingenious overview of biology with emphasis on mathematical ideas—stimulating but requiring careful reading despite the lack of equations."
An anti-aliasing filter (AAF) is a filter used before a signal sampler to restrict the bandwidth of a signal to satisfy the Nyquist–Shannon sampling theorem over the band of interest. Since the theorem states that unambiguous reconstruction of the signal from its samples is possible when the power of frequencies above the Nyquist frequency is ...
In the late 1990s, this work was partially extended to cover signals for which the amount of occupied bandwidth was known, but the actual occupied portion of the spectrum was unknown. [3] In the 2000s, a complete theory was developed (see the section Beyond Nyquist below) using compressed sensing.
The Whittaker–Shannon interpolation formula or sinc interpolation is a method to construct a continuous-time bandlimited function from a sequence of real numbers. The formula dates back to the works of E. Borel in 1898, and E. T. Whittaker in 1915, and was cited from works of J. M. Whittaker in 1935, and in the formulation of the Nyquist–Shannon sampling theorem by Claude Shannon in 1949.