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In order to capture an analog signal accurately, the sampling rate must be at least _____ the frequency.

  1. Equal to

  2. Half

  3. Ten times

  4. Twice

The correct answer is: Twice

To accurately capture an analog signal, the sampling rate must be at least twice the frequency of the signal, according to the Nyquist-Shannon sampling theorem. This principle states that if you want to capture a continuous signal without losing information, you need to sample it at a frequency that is at least double the highest frequency component of the signal. This allows for proper reconstruction of the signal during the playback, preventing the loss of data and ensuring that the original analog signal can be represented accurately in its digital form. Sampling at this rate helps to eliminate aliasing, which occurs when higher frequency signals are misrepresented as lower frequency signals due to insufficient sampling. If the sampling rate is lower than this threshold, there could be distortion and loss of critical information from the signal, which would lead to poor audio or visual quality. Other options such as equal to or ten times the frequency do not adhere to the guidelines set forth by the Nyquist theorem, making them less appropriate for accurately capturing the essential characteristics of analog signals.