If Fc equals Fs/2, what does this imply about the filter's passband with respect to the sampling rate?

• A. It allows up to half the sampling frequency in the baseband.
• B. It allows frequencies above the sampling frequency.
• C. It stops all frequencies.
• D. It has no relation to the sampling frequency.

Answer: (A)

Nyquist frequency sets the upper limit for alias-free representation. When sampling at Fs, the highest frequency that can be represented without aliasing is Fs/2. If the filter’s cutoff is Fs/2, its passband includes all frequencies from 0 up to this Nyquist limit, i.e., it passes the entire baseband up to half the sampling rate. Frequencies above Fs/2 would alias back into the 0 to Fs/2 range unless they’re suppressed, so the filter is effectively limiting itself to the baseband up to Nyquist. That’s why this implies the passband reaches half the sampling rate.