In a nutshell, do a spline interpolation, resample, and then compute a TFTDFT. You will encounter difficulties if the $t_{k+1}- t_k$ vary over several orders of magnitude because the smallest such gap dictates the interval width for resampling. You will also have immense trouble if the data are noisy - in that case you could try to denoise them first, e.g. using wavelets. Finally you will have to handle endpoint problems.
In a nutshell, do a spline interpolation, resample, and then compute a TFT. You will encounter difficulties if the $t_{k+1}- t_k$ vary over several orders of magnitude because the smallest such gap dictates the interval width for resampling. You will also have immense trouble if the data are noisy - in that case you could try to denoise them first, e.g. using wavelets. Finally you will have to handle endpoint problems.