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6. Consider a causal linear system whose (zero-state) response to an input signal, f(t) = e...

6. Consider a causal linear system whose (zero-state) response to an input signal, f(t) = e −3tu(t), is y(t) = (−e −t + 4e −2t − 3e −3t )u(t). (

a) Find the transfer function H(s) of the system.

(b) Write the differential equation that describes the system.

(c) Plot the pole-zero diagram of system. Is the system stable?

(d) Plot the frequency response of the system, |H(w)|.

(e) Whats the systems zero-state response to another input signal, f1(t) = 2e −5tu(t)?

PLEASE make sure to answer d and e.

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