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Energy versus power signals
Short answer
An energy signal has finite total energy and zero average power (e.g., a rectangular pulse), while a power signal has infinite energy but finite non-zero average power (e.g., a sinusoid A cos(ωt) has P=A²/2).
Differentiate between energy and power signals with examples.
Energy signal: a signal with finite total energy and zero average power. Power signal: a signal with finite non-zero average power and infinite energy.
Energy: E = ∫ |x(t)|² dt over (-∞, ∞)
Power: P = lim (T→∞) (1/2T) ∫ |x(t)|² dt over (-T, T)
| Point | Energy signal | Power signal |
|---|---|---|
| Energy | 0 < E < ∞ | E = ∞ |
| Average power | P = 0 | 0 < P < ∞ |
| Duration | Usually finite / decaying (aperiodic) | Usually periodic or random, lasting for all time |
| Examples | Rectangular pulse, e^(-at)u(t) with a > 0 | Sinusoid A cos(ωt), DC signal, square wave |
| Signal type | Non-periodic, transient | Periodic and some random signals |
A signal cannot be both an energy and a power signal. Some signals such as r(t) = t·u(t) are neither.
Example 1: x(t) = e^(-t)u(t): E = ∫₀^∞ e^(-2t) dt = 1/2 (finite), P = 0, so energy signal.
Example 2: x(t) = A cos(ω₀t): E = ∞ and P = A²/2 (finite), so power signal.
✓ Answer checked by Claude Opus 5.5 (high effort)
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