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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

How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
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
How can I make nanorobot?
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
how can I make nanorobot?
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
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