Consider the transfer function

Excite this transfer function with the following inputs, and collect the respective outputs in a vector y(k), k = 0, 1, . . . , 20. Assume the sampling time T = 0.1 s.

(a) u(k) = sin (10k)

(b) u(k) = 100 sin (10k)

(c) u(k) = sin (10k) + sin (20k)

(d) u(k) = sin (k) + sin (10k) + sin (100k)

(e) u(k) is a unit square wave stretching from k = 0 to k = 2

(f) u(k) is a unit square wave stretching from k = 0 to k = 10

(g) u(k) is a unit step Using y(k) and u(k) for k = 0, 1, . . . , 20, derive the transfer function of the system using least-squares method. Compare each solution to the actual transfer function G(z).

G(z) Z z + 0.3z + 0.1 2