I have two vectors: $\vec{a}$ and $\vec{t}$: $a_k$ is the sampling value taken at $t_k$. I need to do DFT, but the sampling period is irregular. I've learned about Frames but unsure how to use the Duffin–Schaeffer's suggestion for a Frame-function: $\sqrt{\frac{t_{n+1}-t_{n-1}}{2T}}sinc(\frac{\pi}{T}[t-t_n])$.

Does the following operation: $C_n=\sum_k{f(k) sinc(\frac{\pi}{T_k}[t_k-t_n])}$, really do the work to get the coefficients ($C_n$) ? (... pretty sure I misinterpreted the equation somehow ...)

Do I need the preceding $\sqrt{\frac{t_{n+1}-t_{n-1}}{2T}}$ ?