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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

where we get a research paper on Nano chemistry....?
Maira Reply
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
Google
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
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
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
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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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