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or no Sinusoidal component at that frequency<br /> | or no Sinusoidal component at that frequency<br /> | ||
| − | 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. | + | 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. |
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| + | [[File:AliasedSineWaves.JPG|frameless|center|The red sine wave is under-sampled, resulting in the two distinct waves having the same data points. [1]]] | ||
| + | <small>The red sine wave is under-sampled, resulting in the two distinct waves having the same data points. [1]</small> | ||
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| + | Nyquist's Theorem can also be used to prevent excessive oversampling. Of course, there must be some small amount of oversampling, unless one already knows the exact maximum frequency contained in a signal. This is because the exact optimal sample rate, the Nyquist Rate, is a value that must be exceeded in order to fully capture signal information and prevent aliasing. | ||
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[[ Walther MA271 Fall2020 topic21|Back to Walther MA271 Fall2020 topic21]] | [[ Walther MA271 Fall2020 topic21|Back to Walther MA271 Fall2020 topic21]] | ||
Revision as of 18:07, 6 December 2020
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]](/rhea/index.php/File:AliasedSineWaves.JPG)
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, unless one already knows the exact maximum frequency contained in a signal. This is because the exact optimal sample rate, the Nyquist Rate, is a value that must be exceeded in order to fully capture signal information and prevent aliasing.
