One of frequently used signal characteristics are energy and power. In signal theory these therms require additional comments because they are a bit different from these what we are used to use in AC or DC systems.
What is power and energy? If wee connect R resistor to voltage U, then resistor will dissipate some power which is equal P=U2/R. During time T the energy loss on this resistor will be: E= TU2/R.
Now lets say that we ad some signal s() instead of DC voltage. In this case the power will depend on time as signal is time dependent. The therm is called instantaneous power: p(s)=s(t)2/R
in order to calculate energy loss during time T we need to integrate:
Sometimes its is more convenient to calculate 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 formulation and then wee can talk about signal power and energy in signal theory:
Signal energy may be finite and infinite. For instance finite signal will have finite length energy while its level wont go to infinite. Any periodical signal has infinite energy. If signal energy is infinite, then we can only talk about average power over all time axis:
Square root of average power gives root mean square (RMS) of signal:
Well for signals with period T you don’t have to calculate average power or RMS using lim function. This is enough to calculate average values during one period. Read more on [Electrical signal power and energy calculations by example].