I have 2 data sets sampled at regular intervals which represent the input and the output of a system. A quick analysis of the plots shows the following:
- There is a proportional factor between the input and the output.
- There is a delay before a change in the input is observable in the output. This delay depends on the scale of the change: larger changes in the input are observable in the output after a longer delay than smaller changes in the input.
I would like to approximate the system with a function, but I am novice in signal processing and I have no idea how to get started. I don't even know if this is a solvable problem. Any idea? I am comfortable using Matlab/Octave, and computer programming in general.
I can get more data from the system if required, but I cannot control the input. This is because the system is only observable when a PID controller keeps it stable.