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Consider a continuous-time LTI system with the input-output relation given by x(T) dT (2.82) -50 (a) Find the impulse response h(t) of this system. (b) Show that the complex exponential function e is an eigenfunction of the system (c) Find the eigenvalue of the system corresponding to e by using the impulse response h(t) obtained in part (a 2) The continuous-time system shown in Fig. 2-18 consists of one integrator and one scalar multiplier. Write a differential equation that relates the output y(t) and the input x(i). att) e(t) y(t) Fig. 2-18 3) Consider a continuous-time LTI system whose step response is given by (t)-eul) Determine and sketch the output of this system to the input x(t) shown in Fig. 2-15(a) x(r) Fig. 2-151) consider a continuous-time lti system with the input-output relation given by x(t) dt (2.82) -50 (a) find the impulse response h(t) of this system. (b) show that the complex exponential function e is an eigenfunction of the system (c) find the eigenvalue of the system corresponding to e by using the impulse response h(t) obtained in part (a 2) the continuous-time system shown in fig. 2-18 consists of one integrator and one scalar multiplier. write a differential equation that relates the output y(t) and the input x(i). att) e(t) y(t) fig. 2-18 3) consider a continuous-time lti system whose step response is given by (t)-eul) determine and sketch the output of this system to the input x(t) shown in fig. 2-15(a) x(r) fig. 2-15

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