Question: Given the step response for a second-order Butter worth filter as in Problem 2.65c, use the superposition and time-in-variance properties of a linear time-invariant system

Given the step response for a second-order Butter worth filter as in Problem 2.65c, use the superposition and time-in-variance properties of a linear time-invariant system to write down the filter??s response to the input

Problem 2.65c

x(t) = u(t) - 2u (t - T) + u(t - 2T)

where u(t) is the unit step. Plot as a function of t/T for (a) f₃T= 20 and (b) f₃T = 2.

2n f3 27 f3 + sin V2 2n f3 Ys (t) 1 xp u (t) COS V2 V2

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