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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.