Problem 2. (20 marks) Continuous-time Signal Analysis. (a) (9 marks) An LTIC system is specified by the equation Dº(D+1)

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Problem 2 20 Marks Continuous Time Signal Analysis A 9 Marks An Ltic System Is Specified By The Equation Do D 1 1 (46.96 KiB) Viewed 11 times

Problem 2. (20 marks) Continuous-time Signal Analysis. (a) (9 marks) An LTIC system is specified by the equation Dº(D+1)y(t) = (D2 + 2)x(t) (i) (4 marks) Find the characteristic polynomial, characteristic equation, characteristic roots, and characteristic modes of this system. (Hints: For repeated roots r, the corresponding characteristic modes are e" and te".) (ii) (5 marks) Find yo(t), the zero-input component of the response y(t) for t > 0, if the initial conditions are yo(0) = 4, yo(0) = 3, and yo(0) = -1.