Which statement best describes a power signal as given?

Which statement best describes a power signal as given?

• A. Finite energy
• B. Periodic signal
• C. Infinite energy
• D. Random process

Answer: (B)

Power signals have energy that grows without bound over all time, but their average power is finite and nonzero. A periodic signal is a classic example: it repeats forever, so the total energy over all time is infinite, yet the energy per period is finite. If you look at a long time interval that contains many periods, the total energy scales with the number of periods, so the average power is the energy per period divided by the period, a finite nonzero value. That combination—infinite total energy but finite average power—matches the definition of a power signal, and periodic signals fit it perfectly. Finite-energy signals, by contrast, have finite total energy and negligible average power over long times, so they’re energy signals. Infinite energy alone doesn’t specify a power signal, and a random process isn’t the standard deterministic description used for this classification.

Power signals have energy that grows without bound over all time, but their average power is finite and nonzero. A periodic signal is a classic example: it repeats forever, so the total energy over all time is infinite, yet the energy per period is finite. If you look at a long time interval that contains many periods, the total energy scales with the number of periods, so the average power is the energy per period divided by the period, a finite nonzero value. That combination—infinite total energy but finite average power—matches the definition of a power signal, and periodic signals fit it perfectly. Finite-energy signals, by contrast, have finite total energy and negligible average power over long times, so they’re energy signals. Infinite energy alone doesn’t specify a power signal, and a random process isn’t the standard deterministic description used for this classification.