Everything about The Nyquist Frequency totally explained
The
Nyquist frequency, named after the Swedish-American engineer
Harry Nyquist or the
Nyquist–Shannon sampling theorem, is half the
sampling frequency of a
discrete signal processing system. It is sometimes called the
folding frequency, or the
cut-off frequency of a sampling system.
The sampling theorem shows that
aliasing can be avoided if the Nyquist frequency is greater than the
bandwidth, or maximum component frequency, of the signal being sampled.
The Nyquist frequency shouldn't be confused with the
Nyquist rate, which is the lower bound of the sampling frequency that satisfies the Nyquist sampling criterion for a given signal or family of signals. This lower bound is twice the bandwidth or maximum component frequency of the signal.
Nyquist rate, as commonly used with respect to sampling, is a property of a continuous-time signal, not of a system, whereas
Nyquist frequency is a property of a discrete-time system, not of a signal.
The aliasing problem
In principle, a Nyquist frequency just larger than the signal bandwidth is sufficient to allow perfect reconstruction of the signal from the samples. However, this reconstruction requires an unattainable filter that passes some frequencies unchanged while suppressing all others completely (commonly called a
brickwall filter). When attainable filters are used, some degree of
oversampling is necessary to accommodate the practical constraints on
anti-aliasing filters. That is, frequencies close to the Nyquist frequency may be distorted in the sampling and reconstruction process, so the bandwidth should be kept below the Nyquist frequency by some margin that depends on the actual filters used.
For example, audio
CDs have a sampling frequency of 44100
Hz. The Nyquist frequency is therefore 22050 Hz, which is an upper bound on the highest frequency the data can unambiguously represent.
If the chosen anti-aliasing filter (a
low-pass filter in this case) has a
transition band of 2000 Hz, then the
cut-off frequency should be no higher than 20050 Hz to yield a signal with negligible power at frequencies of 22050 Hz and greater.
To avoid
aliasing, the Nyquist frequency must be
strictly greater than the maximum frequency component within the signal. If the signal contains a frequency component at precisely the Nyquist frequency then the corresponding component of the sample values can't have sufficient information to reconstruct the Nyquist component in the
continuous-time signal because of phase ambiguity. In such a case, there would be an infinite number of possible and
different sinusoids (of varying amplitude and phase) of the Nyquist frequency component that are represented by the discrete samples.
Other meanings
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 the signal bandwidth or twice the signal bandwidth the Nyquist frequency; still others refer to the Nyquist rate (twice the signal bandwidth) as Nyquist frequency; these are distinctly minority usages.
Further Information
Get more info on 'Nyquist Frequency'.
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