# 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.

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is this allso about nanoscale material
Almas
are nano particles real
yeah
Joseph
Hello, if I study Physics teacher in bachelor, can I study Nanotechnology in master?
no can't
Lohitha
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William
currently
William
where we get a research paper on Nano chemistry....?
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
has a lot of application modern world
Kamaluddeen
yes
narayan
what is variations in raman spectra for nanomaterials
ya I also want to know the raman spectra
Bhagvanji
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
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Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
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Alexandre
what is the stm
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Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
how did you get the value of 2000N.What calculations are needed to arrive at it
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