Energy and Power of a Signal

[jeffttan]

Hi Guys,

I'd just like to ask what does the Energy of a signal mean? and the power of a signal?

thanks

 

[jonw0224]

I am assuming you know that energy is the ability to do work.

I am also assuming you know that power is energy delivered in a set amount of time (rate of energy delivered).

If you're talking about sound waves, the energy is proportional to pressure and mass of matter moved.

If you're talking about electical signals then it becomes voltage and current.

Power is voltage times current. You can measure power at any instant in time if you measure these two. If you want energy, you have to sum the power up over time (integrate), etc.

In terms of a signal, if it's periodic you can perform these calculations over a single period.

-jonathan

 

[neils_arm_strong]

Hi jeffttan,
See power and energy are related.Power is the energy spent or consumed per unit time.If you assume that a signal x(t) is the voltage across a unit resistor,then the power of the signal is x^2(t).Energy is obtained by integrating the power over the given range of the signal.Simply stating power=energy/time.

 

[jeffttan]

why do we integrate the energy of a signal from - infinity to positive infinity?

 

[jjohn]

n signal processing, the energy Es of a continuous-time signal x(t) is defined as

E_{s} \ \ = \ \ <x(t), x(t)> \ \ = \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 Es would appear as volt2-seconds, which is not dimensionally correct for energy in the sense of the physical sciences. After dividing Es 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.
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Spectral Energy Density

Similarly, the spectral energy density of signal x(t) is

Es(f) = | X(f) | 2

where X(f) is the Fourier transform of x(t).

For example, if x(t) represents the magnitude of the electric field component (in volts per meter) of an optical signal propagating through free space, then the dimensions of X(f) would become volt-seconds per meter and Es(f) would represent the signal's spectral energy density (in volts2-second2 per meter2) as a function of frequency f (in hertz). Again, these units of measure are not dimensionally correct in the true sense of energy density as defined in physics. Dividing Es(f) by Zo, the characteristic impedance of free space (in ohms), the dimensions become joule-seconds per meter2 or, equivalently, joules per meter2 per hertz, which is dimensionally correct in SI units for spectral energy density.
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Parseval's Theorem

As a consequence of Parseval's theorem, one can prove that the signal energy is always equal to the summation across all frequency components of the signal's spectral energy density.