Question

The signal Y (t) = e^-2t u (t) is _______________

(a) Power signal with P∞ = \(\frac{1}{4}\)

(b) Power signal with P∞ = \(\frac{1}{2}\)

(c) Energy signal with E∞ = \(\frac{1}{4}\)

(d) Energy signal with E∞ = 0

This question was posed to me during an internship interview.

Origin of the question is Applications of Signals on Circuits in chapter Signals and Systems Basics of Signals and Systems

Answer 1

Correct choice is (b) Power signal with P∞ = \(\frac{1}{2}\)

Easy explanation: 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.

|Y (t)| < ∞, E∞ = \(\int_{-∞}^∞ |y(t)|^2 \,dt\)

= \(\int_∞^∞ e^{-2t} u(t) \,dt \)

= \(\in_∞^∞ e^{-2t} \,dt = \frac{1}{2}\)

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

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