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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

how do you translate this in Algebraic Expressions
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Shanjida
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
Crystal Reply
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
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Cied
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I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
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Porter
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Uday
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AMJAD
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
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AMJAD
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AMJAD
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Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
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Damian
silver nanoparticles could handle the job?
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Azam
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Uday
I'm interested in Nanotube
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this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
Prasenjit
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Prasenjit Reply
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
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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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