Fourier Transform for Aperiodic Time Series RR Interval (HRV analysis)

I'm trying to do an analysis of time series data of heart rate variation. What I have is recorded is the timing of each pulse, recorded with a sampling rate of f=500Hz (T=0.002s). So for example, if pulses occurred at these timings: timings = [0.006, 1.400, 2.200, 2.8, 3.4] in seconds, then the interbeat intervals (RR intervals) would be the results of each beat subtracted from the one before, so RR = [1.3940, 0.8, 0.6, 0.6]. The time series plot would have the timings on the x-axis starting from the second reading (1.4, 2.2,2.8,3.4) and the RR results on the y-axis. The graph is a little messy and aperiodic. In real life obviously I will use more than 5 readings, this is just for simplicity. A full plot should look a bit like this attached image.

So I want to do fourier transform for this series, but am very confused as to how to do it because these pulses are not in regular intervals. I know that fft, in theory, works on aperiodic signals, but on MATLAB I'm not sure how this translates.

How do I change the above arrays to be suitable to work for fft or a similar function? And how would I use fft or a similar function for this?