Definition of Nyquist’s Theorem
In order to fully understand Nyquist's Theorem, one needs to understand the basics of waves and signals. The frequency of a wave is the rate at which waves are observed; that is, it is the number of complete oscillations of the wave per second. The period of a wave is the inverse of the frequency: it is the number of seconds required for one complete oscillation. The frequency of a wave is measured in Hertz, which is defined as 1/seconds, or cycles per second. The period is thus measured in seconds, sometimes phrased as seconds per cycle.
If a signal contains no frequencies higher than a certain value B, then the all of the necessary information in the signal can be captured with a sampling frequency of 2B or higher. This means that to obtain an accurate "picture" of a signal, the sampling period must be at most half the length of the period of oscillation of the signal. But why is this the case?
