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If we are clever enough, we can use these facts to develop a computational algorithm that can compute the Fourier transform of a time series much fasterthan can be obtained using a brute force DFT algorithm. Fortunately, some very clever people have already developed that algorithm. It goes by the name of theFast Fourier Transform, or FFT algorithm.

Steps in the FFT algorithm

In truth, there are several different forms of the FFT algorithm, and the mechanics of each may be slightly different. At least one, and probably many ofthe algorithms operate by performing the following steps:

  • Decompose an N-point complex series into N individual complex series, each consisting of a single complex sample. The order of the decompositionin an FFT algorithm is rather complicated. It is this order of decomposition, and the order of the subsequent recombination of transformresults that causes the FFT algorithm to be so fast. It is also that order that makes the algorithm somewhat difficult to understand. Note that theprogram that I will discuss later does not implement that special order of decomposition and recombination.
  • Calculate the transform of each of the N complex series, each consisting of a single complex sample. This treats each complex sample as if it islocated at the origin of a complex series. This step is trivial. The real part of the transform of a single complex sample located at the origin ofthe series is a complex constant whose values are proportional to the real and imaginary values that make up the complex sample. Since the complexinput series consists of only one complex sample, there is only one complex value in the complex transform.
  • Correct each of the N transform results to reflect the original position of the complex sample in the input series. This involves the application ofsine and cosine curves to the real and imaginary parts of the transform. This step is usually combined with the recombination step that follows.
  • Recombine the N transform results into a single transform result that represents the transform of the original complex series. This is a verycomplicated operation in a real FFT algorithm. It must reverse the order of decomposition in the first step described earlier. As mentioned earlier, itis the order of the decomposition and subsequent recombination that minimizes the arithmetic operations required and gives the FFT itstremendous speed. The program that I will discuss later does not implement the special order of decomposition and recombination used in an actual FFTalgorithm.

A sample program

I want to emphasize at the outset that this program DOES NOT implement an FFT algorithm. Rather, this program illustrates the underlying signal processingconcepts that make the FFT possible in a form that is more easily understood than is normally the case with an actual FFT algorithm.

Separate processes in an FFT algorithm

In summary, a typical FFT algorithm performs the following processes:

  • Decompose an N-point complex series into N individual complex series, each consisting of a single complex sample.
  • Recognize that the complex transform of a single complex sample is equal to the value of the complex sample.
  • Correct the transform for each complex sample to reflect the original position of the complex sample in the input series.
  • Recombine the N transform results into a single transform result that represents the transform of the original complex series.

Questions & Answers

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
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
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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