Energy (signal processing)

In signal processing, the energy E s {\displaystyle E_{s}} of a continuous-time signal x(t) is defined as the area under the squared magnitude of the considered signal i.e., mathematically E s = ⟨ x ( t ) , x ( t ) ⟩ = ∫ − ∞ ∞ | x ( t ) | 2 d t {\displaystyle E_{s}\ \ =\ \ \langle x(t),x(t)\rangle \ \ =\int _{-\infty }^{\infty }{|x(t)|^{2}}dt} The units of E s {\displaystyle E_{s}\,} will be ( [ units of x ( t ) ] 2 ⋅ s ) {\displaystyle \left(\left[{\text{units of}}\ x(t)\right]^{2}\cdot {\text{s}}\right)} . And the energy E s {\displaystyle E_{s}} of a discrete-time signal x(n) is defined mathematically as E s = ⟨ x ( n ) , x ( n ) ⟩ = ∑ n = − ∞ ∞ | x ( n ) | 2 {\displaystyle E_{s}\ \ =\ \ \langle x(n),x(n)\rangle \ \ =\sum _{n=-\infty }^{\infty }{|x(n)|^{2}}} == Relationship to energy in physics == Energy in this context is not, strictly speaking, the same as the conventional notion of energy in physics and the other sciences.

Source: Wikipedia — Energy (signal processing) (CC BY-SA 4.0)