Signal Theory – Why Signal Power Equals Square of Signal


Is there any logic as to why the power of a signal \$\mathrm{x(t)}\$ is taken as \$\mathrm{x^2(t)}\$?
I searched everywhere and there's no clue. My professor told: "It's a standard result so shut up!"

Best Answer

If the signal is represented as a voltage \$v(t)\$ or a current \$i(t)\$ and it is connected to a (1 ohm) resistor, the power dissipated in the resistor is proportional to \$v^2(t)\$ or \$i^2(t)\$.

Apart from that, defining power as a positive, increasing function of the signal amplitude has useful mathematical properties.