According to Nyquist, for a temperature signal with up to 2 Hz fluctuations, which sampling rate provides a safe margin?

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Multiple Choice

According to Nyquist, for a temperature signal with up to 2 Hz fluctuations, which sampling rate provides a safe margin?

Explanation:
The key idea is to sample fast enough to capture the highest-frequency changes without aliasing. If the temperature signal can fluctuate up to 2 Hz, you need at least twice that frequency in your sampling rate, which is 4 samples per second, to meet the Nyquist criterion. However, in practice you want some extra margin to account for filtering and real-world imperfections. Among the given options, sampling at eight samples per second provides a clear safety margin above the bare minimum, well above the 4 Hz threshold. This larger rate helps ensure accurate reconstruction and reduces the risk of aliasing. Sampling at six or four samples per second would still work mathematically, but they offer less margin, and sampling at two samples per second is far too slow to capture the 2 Hz fluctuations without distortion.

The key idea is to sample fast enough to capture the highest-frequency changes without aliasing. If the temperature signal can fluctuate up to 2 Hz, you need at least twice that frequency in your sampling rate, which is 4 samples per second, to meet the Nyquist criterion. However, in practice you want some extra margin to account for filtering and real-world imperfections. Among the given options, sampling at eight samples per second provides a clear safety margin above the bare minimum, well above the 4 Hz threshold. This larger rate helps ensure accurate reconstruction and reduces the risk of aliasing. Sampling at six or four samples per second would still work mathematically, but they offer less margin, and sampling at two samples per second is far too slow to capture the 2 Hz fluctuations without distortion.

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