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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 of a given function or signal
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.
When a bandpass signal is sampled slower than its Nyquist rate, the samples are indistinguishable from samples of a low-frequency alias of the high-frequency signal. That is often done purposefully in such a way that the lowest-frequency alias satisfies the Nyquist criterion, because the bandpass signal is still uniquely represented and ...
Similarly, Nyquist's name was attached to Nyquist rate in 1953 by Harold S. Black: If the essential frequency range is limited to B {\displaystyle B} cycles per second, 2 B {\displaystyle 2B} was given by Nyquist as the maximum number of code elements per second that could be unambiguously resolved, assuming the peak interference is less than ...
The darker gray areas correspond to undersampling with the maximum value of n in the equations of this section. In signal processing, undersampling or bandpass sampling is a technique where one samples a bandpass-filtered signal at a sample rate below its Nyquist rate (twice the upper cutoff frequency), but is still able to reconstruct the signal.
This formula's way of introducing frequency-dependent noise cannot describe all continuous-time noise processes. For example, consider a noise process consisting of adding a random wave whose amplitude is 1 or −1 at any point in time, and a channel that adds such a wave to the source signal. Such a wave's frequency components are highly ...
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
In mathematics, a rate is the quotient of two quantities, often represented as a fraction. [1] If the divisor (or fraction denominator) in the rate is equal to one expressed as a single unit, and if it is assumed that this quantity can be changed systematically (i.e., is an independent variable), then the dividend (the fraction numerator) of the rate expresses the corresponding rate of change ...