Question

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 1

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.