Question

The signal X (t) = \(e^{j(2t + \frac{π}{6})}\) is ________________

(a) Power signal with P∞ = 1

(b) Power signal with P∞ = 2

(c) Energy signal with E∞ = 2

(d) Energy signal with E∞ = 1

The question was asked in a dream while sleeping

The question is from Periodic and Non-Periodic Signals topic in division Signals and Systems Basics of Signals and Systems

Answer 1

Correct option is (a) Power signal with P∞ = 1

To elaborate: If a signal has E∞ as ∞ and P∞ as a finite value, then the signal is a power signal. If a signal has E∞ as a finite value and P∞ as ∞, then the signal is an energy signal.

|x (t)| = 1, E∞ = \(\int_{-∞}^∞ |x(t)|^2 \,dt = ∞\)

So, this is a power signal not an energy signal.

\(P_∞ = lim_{T→∞} \frac{1}{2T} \int_{-T}^T |x(t)|^2 \,dt = 1.\).