Which statement about energy signals is true?

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 those whose total energy is finite, defined by E = ∫{-∞}^{∞} |x(t)|^2 dt. For such signals, the average power is zero, because P = lim{T→∞} (1/2T) ∫_{-T}^{T} |x(t)|^2 dt, and the integral in the numerator is bounded by the finite energy E while the dividing interval 2T grows without bound. So the true statement is that an energy signal has finite energy and zero average power. The idea is that all the signal’s energy is packed into a finite amount of time, so when you average it over increasingly large time windows, the average power tends to zero. Zero energy would mean the signal is zero almost everywhere, which isn’t an energy signal. Finite energy with nonzero average power cannot happen because the average power of an energy signal must vanish in the infinite-time average. Infinite energy with nonzero average power is outside the definition of an energy signal.