# Why the power of periodic signal is square?

I have DSP in my academics and while going through the video lectures i am stuck regarding power of periodic signal.

Its mentioned as

$$P_{\text{avg}}= \frac{1}{N}\sum_{n=0}^{N-1}|x(n)|^2$$

my doubt is why we have to mention $|x(n)|$ as square ?

Note: I am having format issues please edit my Question and put it in format. thank you.

## 2 Answers

Power or energy are always squared quantities. If you consider simple circuits as an example, then power is $V^2/R$ or $I^2R$ (with $V$ voltage, $I$ current, and $R$ resistance). For time-varying signals, the power or energy is computed by a time average of the squared signal. For stochastic signals, the power is defined by the expectation $E[|x(t)|^2]$, which again is usually estimated by computing time averages. The fact that we're always dealing with squared quantities basically goes back to the definition of energy and power.

Power is proportional to the squared amplitude of a signal. This "power" concept comes from thinking of the signal $x[n]$ as representative of a voltage or current waveform. In that model, the power dissipated by applying $x[n]$ to a one-ohm resistor is the value of $|x[n]|^2$ averaged over one period.