GATE EE 2018 Set 1 — Question 26
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Signals & Systems → LTI Systems → LTI, Causal & Stable Systems
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Question
A continuous-time input signal is an eigenfunction of an LTI system, if the output is
Correct answer
(A) k x(t), where k is an eigenvalue
Solution
By definition, a signal is an eigenfunction of a system if the output is a scalar multiple of the input signal. Mathematically, for a system operator , is an eigenfunction if , where is a constant (possibly complex) known as the eigenvalue. For Linear Time-Invariant (LTI) systems, complex exponentials of the form are eigenfunctions because the output is , where is the transfer function evaluated at . Therefore, if the output is , is an eigenfunction.
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