Signal power and energy calculation

The most common signal characteristics are energy and power. In signal theory, these terms require additional comments because they are different from what we are using in AC or DC systems.

What are power and energy? When we connect the R resistor to voltage U, the resistor will dissipate some power equal to P=U2/R. During time T, the energy loss on this resistor will be E= TU²/R.

Now let us say that we add some signal s() instead of DC voltage. In this case, the power will depend on time as the signal is time-dependent. The term is called instantaneous power: p(s)=s(t)²/R

to calculate energy loss during time T we need to integrate:

Sometimes it is more convenient to evaluate average power during some time T:

When we talk about signal power, we don’t care about R load. Therm Signal power usually is used for comparing different signals. For this, it is agreed to use R=1, then we exclude resistance from the formulation, and then we can talk about signal power and energy in signal theory:

p(t) = s^{2}(t)

Signal energy may be finite and infinite. For instance, a finite signal will have limited length energy while its level won’t go to infinite. Any periodical signal has endless energy. If signal energy is unlimited, then we can only talk about average power overall time axis:

The square root of average power gives the root mean square (RMS) of signal:

For signals with period T, you don’t have to calculate average power or RMS using a LIM function. This is enough to calculate average values during one period. Read more on [Electrical signal power and energy calculations by example].