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What is the following graph if u(t) denotes step function and r(t) denotes ramp function?(a) r(t)(b) r(t)-r(t-50)-u(t-50)(c) r(t)-r(t-50)(d) r(t)-u(t-50)This question was posed to me in my homework.This is a very interesting question from Operations on Signals in section Digital Signal Processing of MATLAB

Answer»

Correct choice is (B) r(t)-r(t-50)-u(t-50)

To elaborate: A RAMP function extends upto infinity. But here, the graph ends a 50 units in time. So, the function has a slope change at t=50 and the new slope is 0. But the function value is 0 FO r t>50 so we need to SUBTRACT the function, resulting at t=50, from a unit step function starting from t=50. Hence, the correct solution is option c only.


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