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^(jωt) x(t), where k is an eigenvalue and e^(jωt) is a complex exponential signal
x(t) e^(jωt), where e^(jωt) is a complex exponential signal
k H(ω), where k is an eigenvalue and H(ω) is a frequency response of the system

Correct answer: k x(t), where k is an eigenvalue

Solution

An eigenfunction of an LTI system is defined as a signal that, when passed through the system, results in a scaled version of itself, represented by k x(t), where k is a constant (eigenvalue). This property indicates that the system's response to the eigenfunction is proportional to the input, maintaining its form.

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