signalenergie

Signalenergie, or signal energy, is a quantity used in signal processing to measure the total energy carried by a signal over time. For a continuous-time signal x(t), the energy is defined as E = ∫_{-∞}^{∞} |x(t)|^2 dt. For a discrete-time signal x[n], the energy is E = ∑_{n=-∞}^{∞} |x[n]|^2, provided the integral or sum converges. Signals with finite E are called energy signals, while signals with finite average power but infinite energy are called power signals.

In practice, many common signals are either energy signals (time-limited waveforms) or power signals (infinite duration with finite average power). A finite-duration rectangular pulse with amplitude A, for example, has energy E = |A|^2 T, where T is its duration. A pure sinusoid x(t) = A cos(ω0 t) has infinite energy and is classified as a power signal, with finite average power P = A^2/2.

Parseval’s theorem links time-domain energy to frequency-domain energy. For continuous-time signals, ∫_{-∞}^{∞} |x(t)|^2 dt = (1/2π) ∫_{-∞}^{∞} |X(jω)|^2 dω, where X(jω) is the Fourier transform of x(t). A similar relation holds for discrete-time signals via the discrete-time Fourier transform. These principles allow computation of energy from the spectrum or from the time signal itself.

Units are joules for continuous-time energy; discrete-time representations depend on sampling and amplitude. The concept is standard in German literature as Signalenergie and is used to classify and analyze signals in engineering contexts.