Instantaneous Power of Real Signals

[CoolDude420]

Homework Statement

Hi,

So I'm taking a communications module and we are being introduced to Energy Signals and Power Signals. Now in the notes, it starts off the chapter by saying
"Suppose a signal x(t) is a real signal"
and then it says
The instantaneous power in x(t) is given by x^2(t)

This may be a stupid question. But how is the power in a signal given by it's square?? Up til now the only power I've encountered is power dissipated in a resistor : P=VI.

Homework Equations

The Attempt at a Solution

 

[CWatters]

Typically the load resistance is constant so I think it goes...

P=VI
I=V/R (from Ohms law)
So..
P=V^2/R

it's because I isn't constant and depends on V.

 

[collinsmark]

In communication theory when one is interested in the power signal, they're really interested in a signal that is proportional to the actual power. So squaring the signal is sufficient to meet that criterion.

If the signal is represented in terms of voltage $v(t)$ then the power signal $v^2(t)$ is proportional to the actual power since $P = V^2/R$ for a constant $R$.

If the signal is represented in terms of current $i(t)$ then the power signal $i^2(t)$ is proportional to the actual power since $P = I^2 R$ for a constant $R$.

So it doesn't really matter in what form the signal is measured/represented. Just square it and you'll get power.

This same idea carries over into digital communication theory and digital signal processing. The signal you're working with might just be a bunch of numbers. For example, the data contained in a .WAV sound file. They're not in units of voltage or current; they're just numbers that represent the signal's amplitude. If you want the power signal just square all of those numbers.