According to the Nyquist sampling theorem, what is the minimum sampling frequency to capture a signal with the highest frequency component f_max without aliasing?

According to the Nyquist sampling theorem, what is the minimum sampling frequency to capture a signal with the highest frequency component f_max without aliasing?

• A. f_s >= f_max
• B. f_s >= 2 f_max
• C. f_s >= f_max/2
• D. f_s >= 4 f_max

Answer: (B)

To avoid aliasing, you must sample at least twice the highest frequency in the signal. When you sample at f_s, the spectrum repeats every f_s, so these repeats will overlap the original spectrum unless the repetition bandwidth fits entirely above f_max. That requires f_s/2 ≥ f_max, i.e., f_s ≥ 2 f_max. At the exact threshold of 2 f_max, perfect reconstruction is possible with ideal filtering, though in practice a bit more than 2 f_max is often used to accommodate non-ideal filters. The other options don’t meet the requirement: f_s = f_max is too slow and causes aliasing, f_s = f_max/2 is far too slow, and f_s = 4 f_max is more than necessary.

To avoid aliasing, you must sample at least twice the highest frequency in the signal. When you sample at f_s, the spectrum repeats every f_s, so these repeats will overlap the original spectrum unless the repetition bandwidth fits entirely above f_max. That requires f_s/2 ≥ f_max, i.e., f_s ≥ 2 f_max. At the exact threshold of 2 f_max, perfect reconstruction is possible with ideal filtering, though in practice a bit more than 2 f_max is often used to accommodate non-ideal filters. The other options don’t meet the requirement: f_s = f_max is too slow and causes aliasing, f_s = f_max/2 is far too slow, and f_s = 4 f_max is more than necessary.