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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.


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


Take a look at

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

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.
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
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
characteristics of micro business
for teaching engĺish at school how nano technology help us
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
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
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.
what is the actual application of fullerenes nowadays?
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.
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.
is Bucky paper clear?
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
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.
Do you know which machine is used to that process?
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
On having this app for quite a bit time, Haven't realised there's a chat room in it.
what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
many many of nanotubes
what is the k.e before it land
what is the function of carbon nanotubes?
I'm interested in nanotube
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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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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