Energy (signal processing)
In signal processing, the energy of a continuous-time signal x(t) is defined as
the energy of a discrete-time signal x(t) is defined as
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. The two concepts are, however, closely related, and it is possible to convert from one to the other:
For example, if x(t) represents the potential (in volts) of an electrical signal propagating across a transmission line, then Z would represent the characteristic impedance (in ohms) of the transmission line. The units of measure for the signal energy would appear as volt2·seconds, which is not dimensionally correct for energy in the sense of the physical sciences. After dividing by Z, however, the dimensions of E would become volt2·seconds per ohm, which is equivalent to joules, the SI unit for energy as defined in the physical sciences.
Spectral energy density