Question

When is a complex exponential signal sinusoidal?

(a) σ =0 and Ω = 0

(b) σ < 0 and Ω = 0

(c) σ = 0 and Ω ≠ 0

(d) σ ≠ 0 and Ω ≠ 0

I got this question during an internship interview.

My question comes from The Complex Exponential topic in chapter Signals and Systems Basics of Signals and Systems

Answer 1

The correct option is (c) σ = 0 and Ω ≠ 0

To explain I would say: A signal is sinusoidal when σ = 0 and Ω ≠ 0

⇒ x(t) = e^st = e^(σ+jΩ)t = e^σt e^jΩt = e^jΩt = cosΩt + jsinΩt which is sinusoidal.