What is the impulse response till t=16 unit in time of a system whose transfer function is that of the following?(a) ^3⁄4*r(t-4) + ^3⁄4*r(t-16)+u(t-16)(b) ^3⁄4*r(t-4) – ^3⁄4*r(t+16)-u(t-16)(c) ^3⁄4*r(t-4) – ^3⁄4*r(t-16)-u(t-16)(d) ^3⁄4*r(t-4) – ^3⁄4*r(t+16)-u(t+16)This question was posed to me in my homework.Query is from Impulse Response in division Control System Applications of MATLAB

What is the impulse response till t=16 unit in time of a system whose

1.	What is the impulse response till t=16 unit in time of a system whose transfer function is that of the following?(a) ^3⁄4r(t-4) + ^3⁄4r(t-16)+u(t-16)(b) ^3⁄4r(t-4) – ^3⁄4r(t+16)-u(t-16)(c) ^3⁄4r(t-4) – ^3⁄4r(t-16)-u(t-16)(d) ^3⁄4r(t-4) – ^3⁄4r(t+16)-u(t+16)This question was posed to me in my homework.Query is from Impulse Response in division Control System Applications of MATLAB
Answer» The correct choice is (c) ^3⁄4R(t-4) – ^3⁄4r(t-16)-u(t-16) Best EXPLANATION: The correct representation of the signal shown in the GRAPH is ^3⁄4r(t-4) – ^3⁄4r(t-16)-u(t-16). This is because the ramp function, starting from t=4 units in time, has a slope of ^3⁄4 and it’s shown to END at t=16. So, there it faces a slope change to 0, so the 2^nd term happens and FINALLY, the amplitude becomes 0 which is why, the 3^rd term happens.

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