Which statement about energy signals is true?

Which statement about energy signals is true?

• A. An energy signal has zero energy.
• B. It has finite energy and zero average power.
• C. The energy of a signal is always finite.
• D. An energy signal has infinite energy and nonzero average power.

Answer: (B)

Energy signals have finite energy and zero average power. The energy is defined as E = ∫{-∞}^{∞} |x(t)|^2 dt, which must be finite for an energy signal. The average power is P = lim{T→∞} (1/2T) ∫_{-T}^{T} |x(t)|^2 dt, and for an energy signal this limit is zero because the total energy is concentrated over a finite interval (or decays so quickly that the total energy is finite) while the time window grows without bound.

This is why the statement that the signal has finite energy and zero average power is the correct characterization of an energy signal. The other possibilities conflict with these definitions: having zero energy would imply a trivial signal that is zero almost everywhere, not a general energy signal; saying the energy is always finite ignores that a signal can carry infinite energy if it extends for all time without decay (a power signal); and claiming infinite energy with nonzero average power contradicts the finite-energy nature of energy signals.