Question 8-38D3

To prevent aliasing and ensure a practical filter can effectively remove undesired components after analog-to-digital conversion, the sampling frequency must be **greater than two times the highest component of the sampled frequency**. This is based on the Nyquist-Shannon sampling theorem. It states that to accurately represent an analog signal in digital form, the sampling rate must be at least twice the highest frequency component present in the signal (the Nyquist rate). For *practical* filters, however, a sampling frequency *greater than* this theoretical minimum is required. Real-world anti-aliasing filters have a finite transition band and cannot achieve an infinitely sharp cutoff. This extra margin ensures that the filter has room to adequately attenuate frequencies above the desired signal bandwidth *before* they are sampled, preventing them from "folding back" into the desired spectrum (aliasing), where they would become indistinguishable from actual signal components and be impossible to remove. Options A and D would lead to severe aliasing and loss of information. Option B provides the theoretical minimum but is insufficient for the non-ideal characteristics of practical filters.