 Solution

ID: past-exam-of-the-year-2-of-the-earth-sciences-geology-course-of-the-university-of-oxford/2024/paper-3/8/a/iii/solution

The conventional Nyquist frequency is

f_{N} = f_{s} /2 = 0.75 da y^{- 1}, T_{N} = 1/ f_{N} = 32 h .

Frequencies above this cutoff are indistinguishable from lower-frequency sampled sinusoid aliases. The Nyquist–Shannon sampling theorem requires a band limit strictly below the cutoff for general phase information: at exactly the cutoff, some phases can give zero samples. Thus

32

hours is the conventional limiting period, with unambiguous reconstruction requiring a longer period under those sampling assumptions.

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