Firstly apologise if I use the wrong terminology, I don't have formal experience in signal processing, hence I would appreciate the help a lot. I have a time-domain photon counting signal which due to experimental limitation has 256 time bins. This is considered quite 'scarce' in my field, and analysis is difficult. Signals with at least 1024 time bins would be a lot easier to analyse as they will also obviously have more counts.
Is there any method in signal processing where a known "scarce" signal can be extrapolated to a more "dense" signal? I don't mean extrapolating along the time axis, more like "filling in the gaps" either by being provided an expected model/shape/fit, or by guessing the shape itself?
Any suggestions what to look for in terms of terminology would still be very useful!
Edit(more info): the signal is an exponential decay characterised by a Poisson distribution. The technique is referred to as time-correlated single photon counting (TCSPC) and essentially measures the number of excited photons in a series of time bins. More time bins, more information on the decay behaviour of the photons.