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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.
missing image

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.
missing image

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.

Questions & Answers

what is the stm
Brian Reply
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?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
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
what is Nano technology ?
Bob Reply
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?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
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?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
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?
Damian Reply
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
How can I make nanorobot?
Lily
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
how can I make nanorobot?
Lily
what is fullerene does it is used to make bukky balls
Devang Reply
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
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Source:  OpenStax, Digital signal processing - dsp. OpenStax CNX. Jan 06, 2016 Download for free at https://legacy.cnx.org/content/col11642/1.38
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