Question: Consider a sampled-data system with T = 0.5 s and the characteristic equation given by (a) Find the terms in the system natural response. (b)

Consider a sampled-data system with T = 0.5 s and the characteristic equation given by

(a) Find the terms in the system natural response.
(b) A discrete LTI system is stable, unstable, or marginally stable. Identify the type of stability for
this system.
(c) The natural response of this system contains an undamped sinusoidal response term of the form
A cos(ωkT + θ). Find the frequency ω of this term.

(z-0.9)(z-0.8) (2 -1.9z+1.0) = 0

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