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The Nyquist Sampling Theorem

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The same waveforms, viewed over 20 s instead of 2 s look like this:

3   waveforms over 20 s

Notice how the waveforms drift in and out of phase with each other. At 10 s and 20 s, all the waveforms pass through zero.

Exercise: How many full cycles of each waveform occur between t = 0 and t = 10? How about between
t = 0 and t = 20?  .

As is easily seen, when we take numerous data points during a cycle of the waveform, we can accurately trace out its shape. In the examples above, we are sampling slow waveforms (<20 Hz) at a frequency (100 Hz) greater than any of the contributing frequencies. What happens if the sampling occurs at a frequency similar to or less than the frequency of the observed waveform?

   
 

 

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