= Solution
The conventional <Nyquist frequency> is
$$
\boxed{f_N=f_s/2=0.75\,\mathrm{day^{-1}},\qquad T_N=1/f_N=32\,\mathrm h.}
$$
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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