LTI Impulse Response Estimation with Point Process Input

[Alexei_Nomazov]

Hello,

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?

Thanks,
Alexei Nomazov,
Algorithms Researcher.

 

[fresh_42]

Maybe this could help: https://web.stanford.edu/class/archive/ee/ee278/ee278.1152/lect08-1.pdf

There are a lot of studies on the internet, if you search for lti system power spectral density