Features of Nyquist's Theorem

Aliasing
Oversampling
Some say:
Strictly less than half of the frequency
or no Sinusoidal component at that frequency

Nyquist's Theorem has many features that are important to know when applying the theorem, such as aliasing. Though aliasing has already been mentioned briefly, it will be further explained here, along with its opposite, oversampling. Aliasing is the under-sampling of a signal. The main purpose of using Nyquist's Theorem is to eliminate any aliasing that may occur. As shown below on a simple sine wave signal in the time domain (time is on the x-axis), sampling with a sample rate less than twice the frequency of even just one of two signals could result in two signals appearing to be the same. Aliasing can be prevented with a variety of anti-aliasing tools, such as low-pass filters that filter out high frequencies.

The red sine wave is under-sampled, resulting in the two distinct waves having the same data points. [1]

Nyquist's Theorem can also be used to prevent excessive oversampling. Of course, there must be some small amount of oversampling, in order to prevent aliasing. The image below represents a case of excessive oversampling. The sample rate is much higher than the Nyquist Rate, which is not necessarily a horrible thing. However, the frequency of this signal could easily be found with a much lower sampling rate. Though it might be "nice" to have a detailed idea of the looks of the exact waveform, this high sample rate would likely result in large amounts of unnecessary data that would take more time to analyze.

This degree of oversampling would only increase the amount of time necessary to analyze the signal. [5]
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