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Defines energy and power as ways to measure a signal.

The idea of the "size" of a signal is crucial to many applications. It is nice to know how much electricity can beused in a defibrillator without ill effects, for instance. It is also nice to know if the signal driving a set of headpones isenough to create a sound. While both of these examples deal with electric signals, they are clearly very different signalswith very different tolerances. For this reason, it is convenient to quantify this idea of "size". This leads to theideas of signal energy and signal power.

Signal energy

Since we often think of signal as a function of varying amplitude through time, it seems to reason that a goodmeasurement of the strength of a signal would be the area under the curve. However, this area may have a negative part.This negative part does not have less strength than a positive signal of the same size (reversing your grip on the paper clipin the socket is not going to make you any more lively). This suggests either squaring the signal or taking its absolutevalue, then finding the area under that curve. It turns out that what we call the energy of a signal is the area under the squared signal.

The energy of this signal is the shaded region.
E f t f t 2

Signal power

Our definition of energy seems reasonable, and it is. However, what if the signal does not decay? In this case wehave infinite energy for any such signal. Does this mean that a sixty hertz sine wave feeding into your headphones is asstrong as the sixty hertz sine wave coming out of your outlet? Obviously not. This is what leads us to the idea of signal power .

A simple, common signal with infinite energy.

Power is a time average of energy (energy per unit time). This is useful when the energy of the signal goes to infinity.

P f T 1 T t T 2 T 2 f t 2

We compute the energy per a specific unit of time, then allow that time to go to infinity.
  • Compute Energy T
  • Then look at T Energy T

P f is often called the mean-square value of f . P f is then called the root mean squared ( RMS ) value of f .

Energy vs. power

  • "Energy signals" have finite energy.
  • "Power signals" have finite and non-zero power.

Are all energy signals also power signals?

No. In fact, any signal with finite energy will have zero power.

Are all power signals also energy signals?

No, any signal with non-zero power will have infinite energy.

Are all signals either energy or power signals?

No. Any infinite-duration, increasing-magnitude function will not be either. (eg f t t is neither)

Questions & Answers

Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
AMJAD
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Signal and information processing for sonar. OpenStax CNX. Dec 04, 2007 Download for free at http://cnx.org/content/col10422/1.5
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