What occurs when a 60 cycle sine wave is sampled at 100 Hz?

When a 60 cycle sine wave is sampled at 100 Hz, aliasing occurs because the sampling frequency (100 Hz) is not high enough to accurately capture the sine wave's frequency (60 Hz). According to the Nyquist Theorem, the sampling rate must be at least twice the maximum frequency of the signal being sampled to avoid aliasing. In this case, the Nyquist frequency would be 120 Hz (twice of 60 Hz). Since 100 Hz is below this threshold, the sampled signal will not accurately reflect the original sine wave; instead, it will produce an erroneous interpretation of the signal.

Aliasing leads to distortion in the sampled data, where higher frequency components of a signal can be misrepresented as lower frequencies, causing confusion and miscalculations in the analysis of the signal. Consequently, this incorrect representation can affect any digital processing or interpretation of the signal that follows. The phenomenon can be recognized in various signal processing scenarios, particularly when the sampling rate is inadequate in relation to the frequency content of the signal.