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.
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.
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.
