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\ddot{f}_k = \frac{\dot{f}_{\rm end} - \dot{f}_{\rm start}}{\Delta t},  \end{equation}  where $t_k$ is the central time of the Fourier transformed data, $\Delta t$ is the length of the data, and  \begin{equation} \begin{align}  \dot{f}_{\rm start} = =&  \ddot{\delta}(t_{\rm s})\left( \sum_{l=0} \frac{f^{(l)}}{l!}\left(t_{\rm s} - t_0 +\delta(t_{\rm s}) \right)^l \right) + \nonumber \\  &+  (1+\dot{\delta}(t_{\rm s}))^2 \left( \sum_{l=0} \frac{f^{(l)}}{(l-1)!} \left(t_{\rm s} - t_0 +\delta(t_{\rm s}) \right)^{l-1}\right)  \end{equation} \right)^{l-1}\right),  \end{align}