GATE 2014 EE (EE1) – Question 43

Signals and Systems · Representation of continuous and discrete time signals, shifting and scaling properties · 2 marks · Multiple choice

Which expression represents the function shown, with unit step u(t)?

Diagram for GATE 2014 EE (EE1) question 43

$u(t)-u(t-T)+\frac{t-T}T u(t-T)-\frac{t-2T}T u(t-2T)$
$u(t)+\frac tT u(t-T)-\frac tT u(t-2T)$
$u(t)-u(t-T)+\frac{t-T}T u(t)-\frac{t-2T}T u(t)$
$u(t)+\frac{t-T}T u(t-T)-2\frac{t-2T}T u(t-2T)$

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Correct answer: (A) $u(t)-u(t-T)+\frac{t-T}T u(t-T)-\frac{t-2T}T u(t-2T)$

Explanation

Start with u(t)−u(t−T), which produces the unit pulse from0toT. Add the delayed ramp(t−T)u(t−T)/T, then subtract(t−2T)u(t−2T)/Tto stop its growth at2T. This yields the shown constant1after2T, matching **A**.