What is the minimum sampling frequency for a signal with the highest frequency component fmax, according to Nyquist, and what is the purpose of an anti-aliasing filter?

• A. Fs ≥ 2 fmax; include an anti-aliasing low-pass filter to remove frequencies above Fs/2.
• B. Fs ≥ fmax; to preserve all high-frequency content.
• C. Fs ≤ 2 fmax; to remove DC offset.
• D. Fs ≥ 4 fmax; to reduce quantization noise.

Answer: (A)

The main idea is Nyquist sampling: to faithfully reconstruct a signal that has a highest frequency component fmax, you must sample at least twice that rate. So the minimum sampling frequency is Fs ≥ 2 fmax. Before you sample, you typically apply an anti-aliasing filter, a low-pass filter that removes frequency content above the Nyquist frequency (Fs/2). If those higher frequencies aren’t filtered out, they will fold into the baseband when sampled, causing aliasing and distortion in the reconstructed signal. That’s why the correct approach is to sample at least at 2 fmax and to include a low-pass anti-aliasing filter to eliminate everything above Fs/2. Sampling at fmax wouldn’t prevent aliasing, the anti-aliasing filter isn’t about removing DC offset, and oversampling to 4 fmax isn’t required for this purpose—quantization noise is addressed by resolution, not the anti-aliasing filter.