An analog averager can be represented by the differential equation where y(t)is its output and x(t)the input.
Question:
where y(t)is its output and x(t)the input.
(a) If the input-output equation of the averager is
Show how to obtain the above differential equation and that y(t)is the solution of the differential equation.
(b) If x(t) = cos(Ït) u(t), choose the value of Tin the averager so that the output y(t) = 0 in the steady state. Graphically show how this is possible for your choice of T. Is there a unique value for T that makes this possible? How does it relate to the frequency Ω0 = Ï of the sinusoid?
(c) Use the impulse response h(t) of the averager, to show using Laplace that the steady state is zero when x(t) = cos(Ït) u(t) and T is the above chosen value. Use MATLAB to solve the differential equation and to plot the response for the value of T you chose.
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