# 4.7 Java1491-2d fourier transforms using java, part 2  (Page 18/21)

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## Case 7

Now we are going to make a major change in direction. All of the surfaces from cases 0 through 6 consisted of a few individual points located in specificgeometries in the space domain. All of the remaining points on the surface had a value of zero. This resulted in continuous (but sampled) surfaces in the wavenumber domain.

Now we are going to generate continuous (but sampled) surfaces in the space domain. We will generate these surfaces as sinusoidal surfaces (similar to a sheet of corrugated sheet metal) or the sums of sinusoidal surfaces.

Performing Fourier transforms on these surfaces will produce amplitude spectra consisting of a few non-zero points in wavenumber space with theremaining points in the spectrum having values near zero.

## Need to change the surface plotting scale

In order to make these amplitude spectra easier to view, I have modified the program to cause the square representing each point in the amplitude spectrum to be five pixels on each side instead of three pixels on each side. To keep theoverall size of the images under control, I reduced the width and the height of the surfaces from 41 points to 23 points.

## Display fewer results

I suspect that you have seen all the real parts, imaginary parts, and unshifted amplitude spectra that you want to see. Therefore, at this point, Iwill begin displaying only the input surface, the amplitude spectrum, and the output surface that results from performing an inverse Fourier transform on thecomplex spectrum.

## A zero frequency sine wave

The first example in this category is shown in Figure 12 . The input surface for this example is a sinusoidal wave with a frequency of zero. This results ina perfectly flat surface in the space domain as shown in the leftmost image in Figure 12 . This surface is perfectly flat and featureless.

Figure 12. Graphic output for Case 7.

## The code for this case

The code that was used to generate this surface is shown in Listing 18 . For the case of a sinusoidal wave with zero frequency, every point on the surfacehas a value of 1.0.

Listing 18. Code for Case 7.
```case 7: for(int row = 0; row<rows; row++){ for(int col = 0; col<cols; col++){ spatialData[row][col] = 1.0;}//end inner loop }//end outer loopbreak;```

## A single point at the origin

As shown by the center image in Figure 12 , the Fourier transform of this surface produces a single point at the origin in wavenumber space. This isexactly what we would expect.

## The inverse transform output is ugly

The result of performing an inverse Fourier transform on the complex spectrum is shown in the rightmost image in Figure 12 . As was the case earlier in Figure 6 , the ugliness of this plot is an artifact of the 3D plotting schemeimplemented by the class named ImgMod29 . The explanation that I gave there applies here also.

## A very small error

Once again, the total error is very small. The numeric output shows that the final output surface matches the input surface to within an error that is lessthan about one part in ten to the thirteenth power. Thus, the program produces the expected results for this test case.

#### Questions & Answers

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
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
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.
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
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
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
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
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
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