To capture an analog signal accurately, the sampling rate must be at least ________ the frequency?

The requirement for the sampling rate to be at least twice the frequency of the analog signal is based on the Nyquist theorem. This principle states that to accurately reconstruct an analog signal from its samples, the sampling rate must be at least twice the highest frequency present in the signal. This ensures that all the necessary data points are captured to recreate the original waveform without aliasing, which occurs when higher frequency components are misrepresented in the sampled data.

When the sampling rate is below this threshold, important frequency components may be missed, resulting in a distorted or incorrect representation of the original signal. Choices involving three times the frequency or equal to the frequency may provide a higher margin for accuracy, but they are not the minimum requirement established by the Nyquist theorem. Similarly, half the frequency is insufficient for adequate sampling since it would violate the fundamental principle of capturing enough data for accurate signal reconstruction.