(a) Verify that for the 3-parameter model example in class, the input u[k] = cos2 (ω0k) results in loss of identifiability. In general, using linear algebra principles, derive the condition that the input u[k] should satisfy.
(b) Examine the identifiability of a first-order LTI system y[k]+a1y[k−1] = u[k]+a1u[k−1] for two different conditions (i) non-zero u[k] and zero y (forced response) and (ii) zero u[k] but non-zero y (free response).
2. The impulse response of a d.t. system is given by g[k] = 2(0.6)k−1 + (0.4)k−1 , k ≥ 1.
a) Plot the impulse and step responses of the system. Is the system causal and stable?
b) Arrive at the frequency response function G(e jω) of the system. Plot the magnitude and phase response of the system.
c) What is an appropriate FIR approximation of the system?
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