Signalenergien

Signalenergien, or signal energy, is a quantitative measure used in signal processing, physics, and engineering to describe the amount of energy carried by a signal. It applies to both continuous-time and discrete-time signals and serves as a basis for comparing and normalizing signals.

For a continuous-time signal x(t), the energy is defined as E = ∫ from -∞ to ∞ of |x(t)|^2 dt. For a discrete-time signal x[n], the energy is E = ∑ from -∞ to ∞ of |x[n]|^2. If these integrals or sums converge to a finite value, the signal is called a finite-energy signal. Signals that do not have finite energy, such as periodic waveforms, are typically characterized by finite average power rather than finite energy.

The average power of a signal is defined for power signals by P = lim T→∞ (1/2T) ∫ from -T to T |x(t)|^2 dt in the continuous case, and P = lim N→∞ (1/2N+1) ∑ |x[n]|^2 for discrete-time signals. A signal can have infinite energy but finite power, which is common for repetitive or continuous transmissions.

In the frequency domain, Parseval’s theorem relates time-domain energy to the frequency-domain representation: E = ∫ |X(f)|^2 df for continuous signals, and E = (1/2π) ∫ |X(ω)|^2 dω for angular frequency, where X is the Fourier transform of x. This connects how signal energy distributes across frequencies.

Applications of signal energy include assessing transmission efficiency, normalizing signal amplitudes, and analyzing the performance of filters and communication systems. The term signalenergien is used primarily in German-language technical literature as the plural form of signalenergie.