Question

An exponentially growing sinusoidal signal is:

(a) σ = 0 and Ω = 0

(b) σ > 0 and Ω ≠ 0

(c) σ < 0 and Ω ≠ 0

(d) σ = 0 and Ω ≠ 0

This question was addressed to me during an online interview.

Question is taken from The Complex Exponential topic in chapter Signals and Systems Basics of Signals and Systems

Answer 1

Correct answer is (b) σ > 0 and Ω ≠ 0

Explanation: A complex exponential signal is sinusoidal when Ω has a definite value i.e., Ω ≠ 0. It can either be growing exponential or decaying exponential based on the value of σ.

∴ A signal is sinusoidal growing exponential when σ > 0 and Ω ≠ 0.