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when it's a good idea to use Prony analysis?

Dear all, I hope you are well. I was looking at my channels of some oscillation, and I was thinking on when it's a good idea to use Prony analysis? I understand that it's better to use if the system is able to regain linearity after some time (which time is reasonable?), but what are the leads/cues that you would look after, if you wanted to use Prony analysis for estimating the damping ratio? likewise, which signal is advisable to look at? namely speed deviation, angle, power output, etc. Thanks!