I am in an undergrad Comm signals class and am having a hard time telling the difference between a function that represents a power signal and a function the respresents an energy signal. I am right in saying that a power signal is going to be sinusoidal and an energy signal is a decaying exponential?
If not, how can you tell the difference between the 2 functions just by looking at them?
I’m not sure exactly what you’re asking, but I’ll try to help. All of this info is from my undergrad Comm Signals book: Modern Digital and Analog Communication Systems, B. P. Lathi, 3rd ed.
Energy and Power are properties of a signal. They will not be functions of time. My book defines Energy as the integral from -infinity to infinity of the square of the signal. To get power, you square the signal, integrate from -T/2 to T/2, multiply by 1/T, and finally find the limit of that as T->infinity. (All integrals are with respect to time.) This should all be in your text, too.
I’m guessing your question relates to recognizing if a given signal has finite Energy or Power. For a signal to have finite Energy, it must go to 0 as t->infinity. For a signal to have finite Power, it must be “periodic or have statistical regularity.”
If your signal is sinusoidal, it is periodic and therfore has finite Power. If your signal is a decaying exponential, it tends to 0 and therefore has finite Energy. These are just examples of signals that have these properties.
IANAEE (electrical engineer), but isn’t the power signal going to be the derivative (with respect to time) of the energy signal?
Power = (d/dt) Energy.
If so, and you were given two graphs of signals, one power, one energy, then the power graph would seem to be the graph that represents the derivative of the other (energy) graph.
But this math may not apply here, I don’t know.
POWER IS NOT ENERGY. “Power” essentially means “energy flow.” As Art M. says above, if you measure the change in energy within a closed surface over time, you can calculate the energy flow passing through that surface. Energy is joules, power is joules per second.
“Power signal” is a misuse of terms. All signals are energy signals.
People frequently use the word “power” to mean “energy.” This mistake is extremely widespread. It probably comes from the fact that your power to perform a task is measured in terms of energy. In everyday language we’d say “the power to lift a huge weight,” while the correct description is “the energy required to lift huge weight.” For example, electric power companies are actually electric energy companies, and they sell quantities of electrical energy, NOT quantities of electric power.
To check for errors about “power”, simply change all occurrences of the word “power” into the more accurate term “energy flow,” and change all Watts into Joules/second. Does a utility company sell quantities of “electric power?” Instead change “power” and ask whether they sell quanties of “electric energy flow.” Obviously they sell ENERGY, not flow. You’re paying for joules, not for joules per second.
So, the difference between a power signal and an energy signal is that “power signal” is incorrect terminology, while “energy signal” is the correct way to say it.
A separate issue: what is the fundamental difference between “power supply” and “signal”? Answer: there is no difference. Kilowatts of energy flow could go into a light bulb, or they could go into a speaker stack at a rock concert. Microwatts could go into an amplifier input, or they could be used to power a tiny amplifier inside a hearing aide.
Plug a loudspeaker directly into a 120VAC outlet. (Use a 2000 watt eight-ohm speaker!) This will work just fine, although the 60HZ tone the speaker puts out will be intensely loud.
IAAEE
The use of the terms “Power” and “Energy” in this context is not the same as the conventional physics use of these terms. Here, “Energy” refers to an arbitrary way to measure a signal’s “size”. It is not a time-dependent function and “Power” in this sense is not its derivative. In fact, the definition I gave is one of several that just happens to be more tractable mathematically and relates to the physics concept of “energy”. Stinkpalm, when you are doing your comm signals homework, do not look in your physics book.
Using the definition I gave you (which should be in your textbook), the “Energy” of a time-dependent voltage signal will have units V[sup]2[/sup]s, not Joules. Since you integrated time out, there is no time derivative. The power will have units V[sup]2[/sup] since you averaged over time, not J/s.
Again, Stinkpalm, in the context of your comm signals course “Energy” and “Power” do not have the traditional definitions. If you are interested in how they relate to traditional “energy” and “power”, consider that the definition of “Energy” I gave you would correspond to physical “energy” if the signal you were given happened to be the instantaneous physical “power” over a 1-ohm resistor.