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When comparing analog vs discrete time, we find that there are many similarities. Often we only need to substitute the variblet with n and integration with summation. Still there are some important differences that we need to know.As the complex exponential signal is truly central to signal processing we will study that in more detail.

Analog

The complex exponential function is defined: x t t . If(rad/second) is increased the rate of oscillation will increase continuously. The complex exponential function is also periodic for any value of. In figure we have plotted t and 3 t (the real parts only). In we see that the red plot, corresponding to a higher value of, has a higher rate of oscillation.

Real parts of complex exponentials.

Discrete time

The discrete time complex exponential function is defined: x n n .

If we increase(rad/sample) the rate of oscillation will increase and decrease periodically.The reason is: 2 k n n 2 k n n , where n,k .

This implies that the complex exponential with digital angular frequencyis identical to a complex exponential with 1 2 , see

Two discrete exponentials that are identical
The rate of oscillation will increase until , then it decreases and repeats after 2. In we see that as we increase the angular frequency towardsthe rate of oscillation increases. If you download the Matlab files included at theend of this module you can adjust the parameters and see that the rate of oscillation will decrease when exceeding(but less than 2).
Two discrete exponentials with different frequency.
We need to consider discrete time exponentials at an (digital angular) frequency interval of 2only.
Low (digital angular) frequencies will correspond tonear even multiplies of. High (digital angular) frequencies will correspond tonear odd multiplies of.

Matlab files

complex_exponential.m

Take a look at

  • Introduction
  • Discrete time signals
  • Analog signals
  • Frequency definitions and periodicity
  • Energy&Power
  • Exercises
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Questions & Answers

how to know photocatalytic properties of tio2 nanoparticles...what to do now
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Maciej
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s. Reply
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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.
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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.
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Mostly, they use nano carbon for electronics and for materials to be strengthened.
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CYNTHIA
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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.
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SUYASH Reply
for screen printed electrodes ?
SUYASH
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s. Reply
of graphene you mean?
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or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
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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
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Yasmin
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AMJAD
what is system testing
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
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anybody can imagine what will be happen after 100 years from now in nano tech world
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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
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how did you get the value of 2000N.What calculations are needed to arrive at it
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Source:  OpenStax, Information and signal theory. OpenStax CNX. Aug 03, 2006 Download for free at http://legacy.cnx.org/content/col10211/1.19
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