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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)?

1. (A) e^(jω₀ t)u(t)
2. (B) cos(ω₀ t)
3. (C) e^(jω₀ t)
4. (D) sin(ω₀ t)

Correct answer: (C) e^(jω₀ t)

Solution

The function e^(j heta) is an eigenfunction of linear time-invariant systems because it maintains its form under linear operations and time shifts, resulting in a scaled version of itself, which is a key characteristic of eigenfunctions.

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