A LTI Impulse Response Estimation with Point Process Input


I am trying to estimate transfer function of unknown LTI system, given output and assumed input as point process.

I have measurement of output, while input, which is assumed to be point process, could be created synthetically using known times and amplitudes.

My questions:
1. What is the best approach to estimate spectrum of synthetic point process signal (a-parametric/parametric/AR...)?
2. Is there theoretical formulation for point process spectrum, which could be used to create numerical instance for my transfer estimation purpose.
3. Is there a way to estimate zero/poles of system given only output measurement and assumptions on input, without calculation of input and output signals spectrums?
4. Is there methodology to estimate number of zeros/poles based on given input and output?

Alexei Nomazov,
Algorithms Researcher.
Thanks for the thread! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post? The more details the better.

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