What is the minimum sample rate required to accurately capture frequencies up to 22.05 kHz?

Question

BlackTom AI · Accepted Answer

Consider the question about sampling to accurately capture frequencies up to 22.05 kHz. The key principle here is the Nyquist–Shannon sampling theorem, which states that to faithfully reconstruct a signal without aliasing, the sampling rate must be at least twice the highest frequency present in the signal.

Option 1: 22.05 kHz. This equals the highest frequency, not twice it. Sampling at this rate would alias frequencies above 11.025 kHz and fail to capture the 22.05 kHz component accurately, so this is insufficient.

Option 2: 44.1 kHz. Twice 22.05 kHz is exactly 44.1 kHz, meeting the Nyquist criterion. This rate provides a safe minimum to capture up to 22.05 kHz without aliasing, assuming ideal conditions and appropriate anti-aliasing filtering prior to sampling.

Option 3: 48 kHz. While 48 kHz is higher than the minimum, offering headroom and is common in audio systems, it is not the minimum required to fulfill the criterion. This means it would also work, but it is not the smallest adequate rate.

Option 4: 96 kHz. This is an even higher rate, well above the minimum. Like 48 kHz, it satisfies the requirement but is not the minimum rate necessary for accurate capture up to 22.05 kHz.

In summary, the lower bound dictated by the Nyquist criterion is 44.1 kHz, since it is exactly twice the highest frequency of interest and prevents aliasing for frequencies up to 22.05 kHz. The other options either undershoot the necessary rate (22.05 kHz) or exceed the minimum while still being valid choices in practice for higher fidelity.

What is the minimum sample rate required to accurately capture frequencies up to 22.05 kHz?单项选择题

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