Which statement correctly defines energy and power signals and their standard formulas?

• A. Energy signals are defined by E = ∫_{−∞}^{∞} |x(t)|^2 dt for CT, and P = lim_{T→∞} (1/2T) ∫_{−T}^{T} |x(t)|^2 dt for CT (with analogous sums for DT).
• B. Energy signal is defined by E = ∫_{−∞}^{∞} |x(t)|^2 dt (CT) and E = ∑_{n} |x[n]|^2 (DT); Power signal is defined by P = lim_{T→∞} (1/2T) ∫_{−T}^{T} |x(t)|^2 dt (CT) or P = lim_{N→∞} (1/(2N+1)) ∑_{n=−N}^{N} |x[n]|^2 (DT).
• C. Energy signal is finite energy, and power signal is finite power.
• D. Energy signal and power signal definitions are identical.

Answer: (B)

The central idea is how we separate a signal’s total energy from its long‑term average power, and how those quantities are computed in both continuous time and discrete time. For a continuous-time signal x(t), the energy is found by integrating the squared magnitude over all time. If that integral is finite, the signal is an energy signal; for a discrete-time signal x[n], the energy is the sum of squared magnitudes over all samples, finite in that case. The power, instead, looks at the average value of |x|^2 over a growing time window: in continuous time the limit of the average power is P = lim_{T→∞} (1/2T) ∫{-T}^{T} |x(t)|^2 dt; in discrete time it’s P = lim{N→∞} (1/(2N+1)) ∑_{n=-N}^{N} |x[n]|^2. These definitions are the standard way to capture finite total energy versus finite average power, in both domains. The best option is the one that lays out both the continuous-time and discrete-time formulas for energy and for power explicitly, removing ambiguity about which domain you’re in. It also aligns with the fact that energy signals have finite energy and power signals have finite average power, while the idea that the two definitions are identical is incorrect.