Consider a causal continuous-time linear time-invariant system with the frequency re- sponse below. H (jw) -...

 

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Consider a causal continuous-time linear time-invariant system with the frequency re- sponse below. H (jw) - 5 + jw 8+6jw-w² (a) Determine a differential equation relating the input x(t) and output y(t). (b) What is the impulse response of the system h(t)? (c) Find the output signal y(t) if the input signal is ä(t) = e−³tu(t). (d) Find the spectrum of the output signal Y (jw) if the input signal is x (t) Do not find y(t). = te -6t cos(wot)u(t). Consider a causal continuous-time linear time-invariant system with the frequency re- sponse below. H (jw) - 5 + jw 8+6jw-w² (a) Determine a differential equation relating the input x(t) and output y(t). (b) What is the impulse response of the system h(t)? (c) Find the output signal y(t) if the input signal is ä(t) = e−³tu(t). (d) Find the spectrum of the output signal Y (jw) if the input signal is x (t) Do not find y(t). = te -6t cos(wot)u(t).