Energy (signal processing)

Signal energy is the sum or integral of a signal’s squared magnitude over its duration. It is finite for finite-energy signals, unlike average power for many sustained signals.

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Discrete-time signal: A sequence of values indexed by integer time steps. Its samples are squared and summed to calculate discrete-time energy.
Energy signal: A signal with finite, nonzero total squared magnitude over its full duration. This is the class of signals characterized directly by finite signal energy.
Energy detector: A detector that decides whether a signal is present by measuring received energy over an observation interval. It uses accumulated squared samples to detect signals without requiring a known waveform.
Average power (signal processing): The long-run average of a signal’s squared magnitude, or its average over a specified interval. Power normalizes squared magnitude by duration, whereas energy accumulates it.
Continuous-time signal: A function whose values vary over a continuous time variable. Its squared magnitude is integrated to calculate continuous-time energy.
Power signal: A signal with finite, nonzero long-run average squared magnitude, often having infinite total energy. It distinguishes sustained signals from finite-energy signals.
Matched filter: A linear filter designed to maximize output signal-to-noise ratio for a known waveform in white noise. Its detection performance is commonly analyzed using the signal’s energy.
Root mean square: The square root of the mean of squared values, used to summarize signal magnitude. RMS describes a typical amplitude level rather than total accumulated energy.
Magnitude (mathematics): A nonnegative measure of the size of a number or vector. Complex signals use squared magnitude, rather than ordinary squaring, in the energy sum.
Energy spectral density: A frequency-domain distribution describing how a finite-energy signal’s energy is spread across frequency. It represents the same total energy by frequency rather than by time.