According to the Nyquist-Shannon sampling theorem, what minimum sampling rate is required to reconstruct a bandlimited signal in ADC design?

• A. At least two times the maximum signal frequency
• B. Equal to the maximum frequency
• C. At least four times the maximum frequency
• D. Any sampling rate above the signal bandwidth is sufficient

Answer: (A)

Sampling converts a continuous signal into a discrete sequence, and for a bandlimited signal the spectrum is confined to a maximum frequency f_max. When you sample at rate f_s, the spectrum repeats every f_s in frequency. To be able to reconstruct the original signal without any overlap (aliasing) between these repeats, the copies must not overlap the baseband. That requires the baseband width to fit inside half the sampling rate, so f_max ≤ f_s/2, i.e., f_s ≥ 2 f_max. This minimum rate is the Nyquist rate and is what ADC designers aim for to allow perfect reconstruction (with an ideal interpolation filter) and avoid aliasing. Sampling at just f_max or any rate only above the bandwidth isn’t sufficient because spectral copies would still overlap; sampling at four times f_max is unnecessarily high for perfect reconstruction, though it can be used for practical reasons such as easing anti-aliasing filter requirements.