The sampling theorem is that when an analog signal is converted to a digital signal, if it is sampled at a frequency higher than twice the frequency contained in the original signal,
It is possible to reproduce the original signal.You need to be careful because you can't just double it. For example, a 2Hz signal should be sampled at a frequency higher than 4Hz.
To put it the other way around, it is a signal that can reproduce up to 1/2 of the sampling frequency, and the frequency of 1/2 of the sampling frequency is called the Nyquist frequency.
As a specific example, when sampling a signal with a 2Hz cycle at 5Hz, which is larger than twice 2Hz, the result is as follows.
Looking at this, even if you sample at a frequency greater than twice, it doesn't look very representative of the original signal.
However, frequency analysis shows that a strong amplitude appears in the 2Hz band, which is the frequency of the original signal, and the original signal can be expressed.
■What is the Aliasing?
What if we sample at a frequency less than twice the original signal? The result of sampling the above signal at 3Hz (0.33 seconds) is as follows.
This looks like a 1Hz signal because the spectral analysis shows a strong amplitude around 1Hz.
In this way, when sampling at a frequency less than twice that of the original signal, the signal has a different frequency from the original signal, which is called aliasing.
An example of aliasing is the phenomenon in which the wheels of a running tire appear to rotate slowly or in the opposite direction, depending on the speed of the car. That is aliasing.
As a method to prevent aliasing, there is a low-pass filter called antialiasing filter, but this does not prevent aliasing that occurs as a result of sampling at a lower frequency than the signal you want to sample as described above.
There may be noise higher than the target signal, and this is to prevent the effects of aliasing on this high frequency noise.
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