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java Graph03 Dsp028

The program named Graph03 is very similar to the program named Graph06 discussed earlier. In fact, the program named Graph06 can be used to produce very similar plots where the sample values are represented by vertical bars instead of being represented byconnected dots. This results in the very interesting display shown in Figure 14 . Each of the vertical bars in Figure 14 represents a computational frequency bin. (Compare Figure 14 with Figure 11 .)

Figure 14. Output from Graph03.
missing image

In any event, Graph03 is so similar to Graph06 that I'm not going to discuss it further. A complete listing of the programnamed Graph03 is provided in Listing 20 near the end of the module.

The transform method of the ForwardRealToComplex01 class

That brings us to the heart of this module, which is the method that actually implements the DFT algorithm and performs the spectral analysis. This is amethod named transform , which is a static method of the class named ForwardRealToComplex01 . You saw this method being called five times in the code in Listing 12 .

Will discuss in fragments

As usual, I will discuss this method in fragments. A complete listing of the class is presented in Listing 21 near the end of the module.

The transform method is a rather straightforward implementation of the concepts that I explained in the earlier module titled Fun with Java, How and Why Spectral Analysis Works . If you have not done so already, I strongly urge you go to back and study that module at this time. Youneed to understand those concepts in order for the code in the transform method to make sense.

A brief description

For those of you who don't have the time to go back and study that module in detail, a brief description of the DFT algorithm follows.

Using a notation that I described in the earlier module, the expressions that you must evaluate to determine the frequency spectral content of a target timeseries at a frequency F are shown in Figure 15 .

Figure 15. Spectral transform expressions.
Real(F) = S(n=0,N-1)[x(n)*cos(2Pi*F*n)] Imag(F) = S(n=0,N-1)[x(n)*sin(2Pi*F*n)]ComplexAmplitude(F) = Real(F) - j*Imag(F) Power(F) = Real(F)*Real(F) + Imag(F)*Imag(F)Amplitude(F) = SqRt(Power(F))

What does this really mean?

Before you panic, let me explain what this means in layman's terms. Given a time series, x(n), you can determine if that time series contains a cosinecomponent or a sine component at a given frequency, F, by doing the following:

  • Create one new time series, cos(n), which is a cosine function with the frequency F.
  • Create another new time series, sin(n), which is a sine function with the frequency F.
  • Multiply x(n) by cos(n) on a point by point basis and compute the sum of the products. Save this value, calling it Real(F). This is an estimate ofthe amplitude, if any, of the cosine component with the matching frequency contained in the time series x(n).
  • Multiply x(n) by sin(n) on a point by point basis and compute the sum of the products. Save this value, calling it Imag(f). This is an estimate ofthe amplitude, if any, of the sine component with the matching frequency contained in the time series x(n).
  • Consider the values for Real(F) and Imag(F) to be the real and imaginary parts of a complex number.
  • Consider the sum of the squares of the real and imaginary parts to represent the power at that frequency in the time series.
  • Consider the square root of the power to be the amplitude at that frequency in the time series. (This is the value that is plotted in Figure 9 , Figure 11 , and Figure 14 .)

Questions & Answers

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
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
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
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
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 ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
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
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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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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