# 4.5 Java1486-fun with java, understanding the fast fourier transform  (Page 13/14)

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Figure 10. The numeric output for Case A.
```Case A Real:1.0 0.923 0.707 0.382 0.0 -0.382 -0.707 -0.923 -1.0 -0.923 -0.707 -0.382 0.0 0.382 0.707 0.923imag: 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.00.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0```

If you plot the real and imaginary values in Figure 10 , you will see that they match the transform output shown in graphic form in Figure 9 .

## Case B code

The code from the main method for Case B is shown in Listing 6 . Note that the input complex series contains non-zero values in both the real and imaginaryparts.

Listing 6. Case B code.
```System.out.println("\nCase B"); double[]realInB = {0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1};double[] imagInB ={0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,-1}; double[]realOutB = new double[16];double[] imagOutB = new double[16]; transform.doIt(realInB,imagInB,2.0,realOutB,imagOutB); display(realOutB,imagOutB);```

## Case B in graphical form

Case B is shown in graphical form in Figure 11 .

Figure 11. Case B in graphical form.

## Case B output in numeric form

The output from the code in Listing 6 is shown in Figure 12 .

Figure 12. Case B output in numeric form.
```Case B Real:1.0 0.923 0.707 0.382 0.0 -0.382 -0.707 -0.923 -0.999 -0.923 -0.707 -0.382 0.0 0.382 0.707 0.923imag: -1.0 -0.923 -0.707 -0.382 0.0 0.382 0.707 0.9231.0 0.923 0.707 0.382 0.0 -0.382 -0.707 -0.923```

If you plot the values for the real and imaginary parts from Figure 12 , you will see that they match the real and imaginary output shown in Figure 11 .

## Case C code

The code extracted from the main method for Case C is shown in Listing 7 .

Listing 7. Case C code.
```System.out.println("\nCase C"); double[]realInC = {1.0,0.923,0.707,0.382,0.0,-0.382,-0.707,-0.923,-1.0,-0.923,-0.707,-0.382,0.0, 0.382,0.707,0.923};double[] imagInC ={0.0,-0.382,-0.707,-0.923,-1.0,-0.923, -0.707,-0.382,0.0,0.382,0.707,0.923,1.0,0.923,0.707,0.382}; double[]realOutC = new double[16];double[] imagOutC = new double[16]; transform.doIt(realInC,imagInC,16.0,realOutC,imagOutC); display(realOutC,imagOutC);```

The complex input series for Case C is a little more complicated than that for either of the previous two cases. Note in particular that the input complexseries contains non-zero values in both the real and imaginary parts. In addition, very few of the values in the complex series have a value of zero.

(The values of the complex samples actually describe a cosine curve and a negative sine curve as shown in Figure 13 .)

## The graphic form of Case C

Case C is shown in graphic form in Figure 13 .

Figure 13. The graphic form of Case C.

The Fourier transform is reversible

One of the interesting things to note about Figure 13 is the similarity of Figure 13 and Figure 5 . These two figures illustrate the reversible nature of the Fourier transform.

If I had used a positive input real value instead of a negative input real value in Figure 5 , the input of Figure 5 would look exactly like the output in Figure 13 , and the output of Figure 5 would look exactly like the input of Figure 13 .

With that as a hint, you should now be able to figure out how I used a mouse and drew the perfect sine and cosine curves in Figure 13 . In fact, I didn't draw them at all. Rather, I used my mouse and drew the output, andthe applet gave me the corresponding input automatically.

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
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
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
nanocopper obvius
Alexandre
what is the stm
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
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
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
how did you get the value of 2000N.What calculations are needed to arrive at it
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