It is necessary to obtain a discrete$-$time model for a particular system. Two responses have been obtained: the first response is an impulse response, and the second response is the response to a chirp. The data for these responses can be found in two files "Control System Theory Impulse Response Data.txt$"$ and "Control System Theory Chirp Data.txt$"$ uploaded to the course Brightspace page. It is suspected that the system is lower order than sixth order, but it is not known for sure.

$($A$)$ Obtain a model for this data. Use one of the two system identification methods we discussed in class. The chosen identification method will use one set of the data.

$($B$)$ Determine the eigenvalues of the model that you obtained.

$($C$)$ Validate your model by exciting the model with the input used in the "other" data. That is$,$ if the chirp was used to create the model, compare the impulse response of your model to the chirp$-$response data; if the impulse response was used to create the model, compare the chirp response of your model to the impulse$-$response data.