The Nyquist theorem states that the sampling frequency must be less than twice the frequency of the input signal.

• A. True
• B. False
• C. Not specified
• D. Depends on the signal

Answer: (B)

The essential idea is that the Nyquist rate provides a lower bound on how fast you must sample, not a limit on how fast you must avoid sampling. To capture all information from a signal with the highest frequency component fmax, the sampling frequency must be at least twice fmax. If you sample slower than 2 fmax, different frequency components can masquerade as lower frequencies when you reconstruct, causing aliasing and distortion. In practice, you typically sample somewhat above 2 fmax and use an anti-aliasing filter to remove frequencies above fmax before sampling. So the statement is false because the requirement is to be at least twice the highest frequency, not less. For example, a 10 kHz signal needs a sampling rate of at least 20 kHz to avoid aliasing.