Signal and System: Energy Signal

In signal processing, the energy

E s

of a continuous-time signal x(t) is defined as

$E_{s} \ \ = \ \ \langle x(t), x(t)\rangle \ \ = \int_{-\infty}^{\infty}{|x(t)|^2}dt$

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:

$E = {E_s \over Z} = { 1 \over Z } \int_{-\infty}^{\infty}{|x(t)|^2}dt$

where Z represents the magnitude, in appropriate units of measure, of the load driven by the signal.

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 $E s$ would appear as volt²-seconds, which is not dimensionally correct for energy in the sense of the physical sciences. After dividing $E s$ 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.

Signal and System

Saturday, September 19, 2009

Energy Signal

No comments:

Post a Comment