# 4.7 Java1491-2d fourier transforms using java, part 2  (Page 13/21)

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Regardless of the fact that the real and imaginary parts are not flat, the square root of the sum of the squares of the real and imaginary parts (the amplitude) should be the same for every point in wavenumber space for this case. Thus, the real and imaginary parts are related in a very special way.

## The code for Case 1

The code that is executed when switchCase equals 1 is shown in Listing 16 .

Listing 16. Code for Case 1.
```case 1: spatialData[2][2] = 1;break;```

This case places a single impulse close to but not at the origin in space. This produces a flat amplitude spectrum in wavenumber space just like in Case 0.However, the real and imaginary parts of the spectrum are different from Case 0. They are not flat. The computations are probably more subject to errors in thiscase than for Case 0.

## The visual output

Figure 6 shows the six output images produced by the program for a switchCase value of 1.

Figure 6. A displaced impulse in space.

## The input and output surfaces match visually

The input and output surfaces showing the single impulse are in the two leftmost images in Figure 6 . From a visual viewpoint, the output at the bottom appears to be an exact match for the input at the top.

## The real and imaginary parts

The real and imaginary parts of the wavenumber spectrum are shown in the two center images. The real part is at the top and the imaginary part is at thebottom.

For a single impulse in the space domain, we would expect each of these surfaces to be a 3D sinusoidal wave (similar to a piece of corrugated sheet metal) . That appears to be what we are seeing, with almost two full cycles of the sinusoidal wave between the origin and the bottom right corner of theimage.

(The distance between the peaks in the sinusoidal wave in wavenumber space is inversely proportional to the distance of the impulse from theorigin in space. Hence, as the impulse approaches the origin in space, the peaks in wavenumber space become further and further apart. When the impulseis located at the origin in space, the distance between the peaks in wavenumber space becomes infinite, leading to flat real and imaginaryparts.)

## Symmetry

We know that the real part of a wavenumber spectrum resulting from the Fourier transform of a real space function is symmetric about the origin. Wealso know that the imaginary part is asymmetric about the origin.

The symmetry/asymmetry requirements appear to be satisfied by this case. The color bands in the real part at the top are symmetric on either side of theorigin.

The imaginary part is asymmetric about the origin (the centers of the red/white and the blue/black bands appear to be equidistant from and on oppositesides of the origin) .

## The amplitude spectrum is ugly

The amplitude spectrum is shown in the two rightmost images in Figure 6 . The unshifted amplitude spectrum is shown at the top. The amplitude spectrum withthe origin shifted to the center is shown at the bottom.

The ugliness of these two plots is an artifact of the 3D plotting scheme implemented by the class named ImgMod29 . In order to maximize the use of the available dynamic range in the plot, eachsurface that is plotted is normalized such that:

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what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
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why?
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?
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
what does nano mean?
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?
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
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
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
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
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?
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
how did you get the value of 2000N.What calculations are needed to arrive at it
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