Question: The impulse response of a continuous-time linear time-invariant system is
h(t) = δ(t) - 0.1e-0.1tu(t)
(a) Find the frequency response H(jω) of the system. Express your answer as a single rational function with powers of (jω) in the numerator and denominator.
(b) Plot the frequency response magnitude squared
|H(jω)|2 = H(jω)H*(jω)
versus ω. Also plot the phase ∠H(jω) as a function of ω.
(c) At what frequency w does the magnitude squared of the frequency response have its largest value? At what frequency is the magnitude squared of the frequency response equal to one half of its peak value? This is referred to as the half-power point of the filter since the magnitude-squared corresponds to power.
(d) Suppose that the input to this system is
x(t) = 10 + 20cos(0.1t) + δ(t - 0.2)
Use superposition to find the output y(t), after finding the response of each term with the easiest method, (impulse response or frequency response).