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.