# 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 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
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da
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Bhagvanji
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
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
yes that's correct
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
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Damian
How we are making nano material?
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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
Is there any normative that regulates the use of silver nanoparticles?
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
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
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