GATE 2018 EE – Question 26
Signals and Systems · Linear time invariant and causal systems · 1 mark · Multiple choice
A continuous-time input signal $x(t)$ is an eigenfunction of an LTI system, if the output is
- $k\,x(t)$, where $k$ is an eigenvalue
- $k\,e^{j\omega t}x(t)$, where $k$ is an eigenvalue and $e^{j\omega t}$ is a complex exponential signal
- $x(t)e^{j\omega t}$, where $e^{j\omega t}$ is a complex exponential signal
- $k\,H(\omega)$, where $k$ is an eigenvalue and $H(\omega)$ is a frequency response of the system
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Correct answer: (A) $k\,x(t)$, where $k$ is an eigenvalue
Explanation
By definition, an eigenfunction is mapped to a scaled copy of itself, $y(t)=k\,x(t)$, with $k$ the eigenvalue.