# Build an inverse model for a train of gaussian pulses

I have a stationary signal from a train of Gaussian pulses. My sampling window is too wide (cannot be reduced). In the example 1 ms. So it is not possible to clearly distinguish one pulse from another.

The advantage is that I can resample the signal several times by moving sampling start with a delay. For example, I sample the signal 5 times, moving 0.2 ms in each one.

I need to build an inverse model that given the sampled signals (the 5 signals below), original signal can be reconstructed.

Is there any algorithm that solves this inverse problem?

• Maybe you can model the arrival of the pulses as a known process such as a poisson arrival process. Then, if you utilize different sampling patterns, you have a set of observations. Finally, you can utilize an estimation methos such as maximum likelyhood estimation in order to estimate the arrival rate of the previously modeled arrival process. Now that you have a model of the process and a set of observations, you can find the train of pulses that maximizes the consistency between the observations and the arrival process model. – strahd Feb 5 at 20:53

On each cycle of the 5 kSps clock, the input is fed into each 5 sample moving average filter ($$MAF5$$) with each filter input delayed by one sample. Once each filter has received 5 samples, the output is decimated by 5, thus providing a new sum over 5 samples, every 5 samples. Each decimated output is offset by one sample. Thus it is clear that each of these outputs is simply the output of the first $$MAF5$$ after each sample of the 5 kSps clock, as shown in the diagram below.