# 4.7 Java1491-2d fourier transforms using java, part 2  (Page 12/21)

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## The getSpatialData method

This method constructs and returns a specific 3D surface in a 2D array of type double . The surface is identified by the value of an incoming parameter named switchCase . There are 14 possible cases. The allowable values for switchCase range from 0 through 13 inclusive.

The other two input parameters specify the size of the surface that will be produced in units of rows and columns.

## The code for the getSpatialData method

The getSpatialData method begins in Listing 14 .

Listing 14. Beginning of the getSpatialData method.
```private static double[][]getSpatialData( int switchCase,int rows,int cols){double[][] spatialData =new double[rows][cols];switch(switchCase){```

Listing 14 begins by creating a 2D array object of type double in which to store the surface.

Then Listing 14 shows the beginning of a switch statement that will be used to select the code to create a surface that matches the valueof the incoming parameter named switchCase .

## Case 0

Listing 15 shows the code that is executed for a value of switchCase equal to 0.

Listing 15. Code for Case 0.
```case 0: spatialData[0][0] = 1;break;```

This case places a single non-zero point at the origin in the space domain. The origin is at the top-left corner. The surface produced by this case is shownin the leftmost image in Figure 5 . The non-zero value can be seen as the small white square in the top-left corner. In signal processing terminology,this point can be viewed as an impulse in space. It is well known that such an impulse produces a flat spectrum in wavenumber space.

Figure 5. An impulse in space.

## The output surface

The rightmost image in Figure 5 shows the result of:

• Performing a forward Fourier transform on the surface in the leftmost image
• Performing an inverse Fourier transform on the complex wavenumber spectrum produced by the forward transform.

You can see the impulse as the small white square in the top-left corner of both images.

## The wavenumber spectrum is flat

Because the wavenumber spectrum is flat, plots of the spectrum are completely featureless. Therefore, I did not include them in Figure 5 .

## A very small error

The numeric output shows that the final output surface matches the input surface to within an error that is less than about one part in ten to thefourteenth power. The program produces the expected results for this test case.

If you were to go back to the equations in Listing 2 and Listing 3 and work this case out by hand, you would soon discover that the computationalrequirements are almost trivial. Most of the computation involves doing arithmetic using values of 1 and 0. Thus, there isn't a lot of opportunity forcomputational errors in this case.

## Case 1

Now we are going to see a case that is more significant from a computational viewpoint. The input surface in this case will consist of a single impulse thatis not located at the origin in the space domain. Rather, it is displaced from the origin.

The wavenumber amplitude spectrum of a single impulse in the space domain should be flat regardless of the location of the impulse in the space domain.However, the real and imaginary parts of the wavenumber spectrum are flat only when the impulse is located at the origin in space.

do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
Abigail
Do somebody tell me a best nano engineering book for beginners?
what is fullerene does it is used to make bukky balls
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
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?
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 ?
for screen printed electrodes ?
SUYASH
What is lattice structure?
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
what's the easiest and fastest way to the synthesize AgNP?
China
Cied
types of nano material
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.
what is nano technology
what is system testing?
preparation of nanomaterial
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
what is system testing
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
Hello
Uday
I'm interested in Nanotube
Uday
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
Prasenjit
how did you get the value of 2000N.What calculations are needed to arrive at it
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