Suppose the input r(t) and output y(t) of a causal system are related by d d...
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Suppose the input r(t) and output y(t) of a causal system are related by d d -x(t) - 3x(t). dt (a) Given that this system is linear and time invariant, show that the transfer function is y(t) + 2y(t) H (w) = = dt Y(w) X (w) = (jw) - 3 (jw) + 2 . (b) Find the impulse response of the system. (c) A system is said to be stable if |h(t) |dt converges. Is this system stable? (3 marks) (2 marks) (2 marks) Suppose the input r(t) and output y(t) of a causal system are related by d d -x(t) - 3x(t). dt (a) Given that this system is linear and time invariant, show that the transfer function is y(t) + 2y(t) H (w) = = dt Y(w) X (w) = (jw) - 3 (jw) + 2 . (b) Find the impulse response of the system. (c) A system is said to be stable if |h(t) |dt converges. Is this system stable? (3 marks) (2 marks) (2 marks)
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a Finding the transfer function To find the transfer functionwe take the Laplace transform of both s... View the full answer
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