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We could also perform experiments on the computer where we caused the weights to vary with frequency, thus, allowing us to design and placedigital filters on the seismometers to optimize the response of the array to earthquake signals while suppressing seismic noise associated with nearbycities and other sources of seismic noise.

A general purpose mathematical transform

I mention all of this simply to illustrate the general nature of the Fourier transform. Once again, the Fourier transform is simply amathematical process that can be used to transform a set of complex values in one domain into a set of complex values in a different domain.

Before getting into the details of this discussion, I want to refer you to a couple of excellent references on the FFT. Of course, you can find manymore by performing a Google search for the keyword FFT.

Fourier transform images

Many of the images that you will see in this module were produced using an applet named FftLab that I originally downloaded from a website named sepwww.stanford.edu/oldsep/hale/FftLab.html. (As of October 2015, that website no longer exists. However, you can now downloadthe applet from (External Link) . Also, as of October 2015, you can learn more about the applet's author, DaveHale here .)

In order to use the applet to create the illustrations for this document, I changed the name of the applet class to cause it to fit into my file-naming scheme. I alsomade a couple of minor modifications to the code to force the applet's output to fit into this narrow publication format. Otherwise, I used the applet in its originalform. This applet is extremely useful in performing FFT experiments very quickly and easily. I strongly recommend that you become familiar with it.

As an alternative to downloading the applet from the web page given above, click here to download a zip file containing the modified source code for the applet along with a Windowsbatch file that will compile and execute the applet. ((Assuming that you have the Java Development Kit (JDK) and Oracle's appletviewer program installed on your computer, you should be able to simply extract thecontents of the zip file into an empty folder and double-click on the batch file to run the applet.)

Will discuss underlying concepts

As mentioned earlier, the FFT algorithm is very complicated. I won't discuss the mechanics of the algorithm in this module. Rather, I willexplain the underlying concepts that make the FFT algorithm possible.

Hopefully after reading my explanation of the basic concepts, you will be able to understand the explanation of the mechanics of the algorithmprovided by others.

A linear transform

The FFT algorithm is an algorithm that takes advantage of several reasonably well-know facts along with some less well-known facts.

One of those facts is that the Fourier transform is a linear transform. By this, I mean that the transform of the sum of two or more input series isequal to the sum of the transforms of the individual input series. I will attempt to illustrate this in Figure 1 , Figure 2 , and Figure 3 .

Questions & Answers

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
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
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
preparation of nanomaterial
Victor Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Digital signal processing - dsp. OpenStax CNX. Jan 06, 2016 Download for free at https://legacy.cnx.org/content/col11642/1.38
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