Which statement best describes the use of energy spectral density and PSD?

• A. They describe energy and power distribution identically
• B. Energy spectral density applies to finite-energy signals; PSD applies to power signals
• C. They are the same concept
• D. PSD applies to finite-energy signals; energy spectral density applies to finite-power signals

Answer: (B)

The key idea is matching the right spectral description to the type of signal you have. If a signal has finite energy (you can integrate its squared magnitude over time and get a finite number), its energy is spread across frequencies, and the energy spectral density describes that spread. This density is typically taken as the squared magnitude of the Fourier transform, S_x(f) = |X(f)|^2, and the total energy of the signal equals the integral of this density over all frequencies. In other words, the area under the energy spectrum tells you how much energy sits at all frequencies combined.

If the signal carries finite average power but infinite energy (a signal that lasts forever, like a constant or a long sine wave), you instead use the power spectral density. The PSD tells you how the signal’s average power is distributed across frequencies. It’s defined in a way that accounts for the long-time behavior (often via a limit of a windowed Fourier transform as the observation window grows), and the total average power equals the integral of the PSD over frequency.

Because these two descriptors apply to different signal types—finite-energy versus finite-power—the statement that energy spectral density applies to finite-energy signals and PSD applies to power signals is the correct framing. The two densities conceptually describe similar ideas (how energy or power is allocated across frequency) but in contexts that are appropriate to the signal’s energy and power properties.