A continuous-time LTI system is represented by the ordinary differential equation

where x(t) is the input and y(t) the output.

(a) Determine the frequency response H(jΩ) of this system by considering the steady-state output of the system to inputs of the form x(t)=e^jΩt, for ˆ’ˆž < Ω < ˆž.

(b) Carefully sketch the magnitude, |H(jΩ)|, and the phase, ˆ H(jΩ), frequency responses of the system. Indicate the magnitude and phase at frequencies of 0, ±1, and ±ˆž rad/sec.

(c) If the input to this LTI is x(t) = sin(t)/(Ï€t), determine and carefully plot the magnitude response |Y(Ω)|of the output, indicating the values at frequencies 0, ±1, and ±ˆž rad/sec.

Transcribed Image Text:

dy(t) dt = -y(t) + x(t) %|