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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 ( bandwidth ) of a given function or 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]
The theorem states that the sample rate must be at least twice the bandwidth of the signal to avoid aliasing. In practice, it is used to select band-limiting filters to keep aliasing below an acceptable amount when an analog signal is sampled or when sample rates are changed within a digital signal processing function.
The Nyquist rate is defined as twice the bandwidth of the signal. Oversampling is capable of improving resolution and signal-to-noise ratio, and can be helpful in avoiding aliasing and phase distortion by relaxing anti-aliasing filter performance requirements. A signal is said to be oversampled by a factor of N if it is sampled at N times the ...
English: This is a 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). They are rarely equal, because that would require over-sampling by a factor of 2 (i.e. 4 times the bandwidth).
Plot of sample rates (y axis) versus the upper edge frequency (x axis) for a band of width 1; grays areas are combinations that are "allowed" in the sense that no two frequencies in the band alias to same frequency. The darker gray areas correspond to undersampling with the maximum value of n in the equations of this section.
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.