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The conventional Nyquist frequency isFrequencies 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.

The true daily component has $f_D=1\mathrm{da}{\mathrm{y}}^{-1}$, above machine 3's Nyquist frequency. At sampling times $t_n=2n/3$ days,The last sequence is also produced by a continuous cosine with frequency $0.5\mathrm{da}{\mathrm{y}}^{-1}$ sampled at those same times. Hence the observed peak is the sampled sinusoid aliasIt is not evidence for an additional two-day physical temperature cycle.