Which statement about energy signals is true?

• A. It has zero energy.
• B. It has finite energy and zero average power.
• C. It has finite energy and nonzero average power.
• D. It has infinite energy and nonzero average power.

Answer: (D)

Energy signals are identified by having finite total energy, defined as E = ∫ |x(t)|^2 dt < ∞. When the total energy is finite, the average power P, given by P = lim_{T→∞} (1/2T) ∫_{-T}^{T} |x(t)|^2 dt, must be zero, because the same finite amount of energy is spread over an ever-growing time interval. On the other hand, a signal with infinite energy and nonzero average power is a power signal (like a periodic signal) that continues to deliver energy at a steady rate, so its energy diverges and its average power stays positive. Therefore, the true statement for energy signals is that they have finite energy and zero average power. The idea that a signal has infinite energy with nonzero average power describes a power signal, not an energy signal, and zero energy would only apply to the trivial zero signal.