# 4.7 Java1491-2d fourier transforms using java, part 2  (Page 20/21)

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(Recall that for the plotting format used in Figure 14 , the color white is reserved for the single point with the highest elevation. Thedifference in an elevation colored white and an elevation colored red for this plotting format might be as small as one part in ten to the fourteenthor fifteenth power. As a practical matter, red and white indicate the same elevation for this plotting format.)

For a sinusoidal surface with eight samples per cycle, we would expect the peaks to occur in the wavenumber spectrum about one-fourth of the distance fromthe origin to the folding wavenumber. Figure 14 meets that expectation.

The peaks are surrounded on both sides by blue and cyan colors, indicating very low values.

## The inverse Fourier transform output

The output from the inverse Fourier transformed performed on the complex spectrum is shown in the rightmost image in Figure 14 . This output compares very favorably with the input surface shown in the leftmost image. The differencebetween the two is that the input has white vertical bands whereas the output has red vertical bands (with a single white spot) . The above explanation of white versus red applies here also.

You can view the code that created this surface in Listing 22 near the end of the module.

## Case 12

This case draws a sinusoidal surface on the horizontal axis with three samples per cycle plus a sinusoidal surface on the vertical axis with eightsamples per cycle as shown by the leftmost image in Figure 15 .

Figure 15. Graphic output for Case 12.

## The wavenumber spectrum

Performing a forward Fourier transform produces symmetrical peaks on the horizontal and vertical axes on all four sides of the wave number origin. Thesepeaks are indicated by the red and white squares in the center image in Figure 15 .

(See the earlier discussion regarding the difference in elevation indicated by red and white for this plotting format.)

The peaks on the vertical axis should be about one-fourth of the way between the origin and the folding wavenumber. This appears to be the case. The peaks onthe horizontal axis should be about two-thirds of the way between the origin and the folding wavenumber, which they also appear to be.

## Inverse Fourier transform output

The output produced by performing an inverse Fourier transform on the complex spectrum is shown in the rightmost image in Figure 15 . Taking the red versus white issue into account, this output compares favorably with the input surface shown in theleftmost image in Figure 15 .

You can view the code that created this surface in Listing 22 near the end of the module.

## Case 13

This case draws a sinusoidal surface at an angle of approximately 45 degrees relative to the horizontal as shown in the leftmost image in Figure 16 . This sinusoid has approximately eight samples per cycle.

Figure 16. Graphic output for Case 13.

## The wavenumber spectrum

Performing a forward Fourier transform on this surface produces a pair of peaks in the wavenumber spectrum that are symmetrical about the origin atapproximately 45 degrees relative to the horizontal axis. These peaks are indicated by the red and white squares in the center image in Figure 16 .

#### Questions & Answers

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
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
can nanotechnology change the direction of the face of the world
how did you get the value of 2000N.What calculations are needed to arrive at it
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