This section defines some useful functions of signals. The energy of a pressure wave is the integral over time of the squared pressure divided by the wave impedance the wave is traveling in. The energy of a velocity wave is the integral over time of the squared velocity times the wave impedance. In audio work, a signal is typically a list of pressure samples derived from a microphone signal, or it might be samples of force from a piezoelectric transducer, velocity from a magnetic guitar pickup , and so on. In all of these cases, the total physical energy associated with the signal is proportional to the sum of squared signal samples.
Power is always in physical units of energy per unit time.
It therefore makes sense to define the average signal power as the total signal energy divided by its length. We normally work with signals which are functions of time. Power, in contrast, is a temporal energy density. Here, we call that the variance . Furthermore, is regarded as the distance between and .