Consider the values of y(k) in Problem 10.6-3 at k = 0, 2, 4, 6, and 8. Using these values and assuming T = 0.2 s, repeat the least-squares estimation of the transfer function. Next, consider the values at k = 0, 4, and 8, and assuming T = 0.4 s repeat the estimation one more time. Compare both of these estimates with that obtained in Problem 10.6-3.

Problem 10.6-3

Consider the following unit step response of a discrete-time LTI system:

It is known that the transfer function of the system has three poles and two zeros. All three poles are at z = 1. Assuming the sampling time T = 0.1 s, derive a least-squares estimate of the transfer function using this prior information.

Transcribed Image Text:

k y(k) 0 0 4 2 -8 3 16 4 -24 5 36 6 -48 7 64 8 -80