GATE 2016 EC – Question 16

Networks, Signals and Systems · LTI Systems · 1 mark · Multiple choice

Which one of the following is an eigen function of the class of all continuous-time, linear, time-invariant systems ($u(t)$ denotes the unit-step function)?

$e^{j\omega_0 t} u(t)$
$\cos(\omega_0 t)$
$e^{j\omega_0 t}$
$\sin(\omega_0 t)$

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Correct answer: (C) $e^{j\omega_0 t}$

Explanation

A complex exponential defined for all time, $e^{j\omega_0 t}$, passes through any linear time-invariant system as the same exponential multiplied by a constant, which is the system's frequency response. Cosines and sines mix two exponentials with different constants, and the step-truncated exponential does not stay in the same form.