<< Chapter < Page
  Digital signal processing - dsp     Page 15 / 24
Chapter >> Page >
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 variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
yes that's correct
I think
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
how nano science is used for hydrophobicity
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
what is differents between GO and RGO?
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
analytical skills graphene is prepared to kill any type viruses .
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
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
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
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.
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
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
Privacy Information Security Software Version 1.1a
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

Get the best Algebra and trigonometry course in your pocket!

Source:  OpenStax, Digital signal processing - dsp. OpenStax CNX. Jan 06, 2016 Download for free at https://legacy.cnx.org/content/col11642/1.38
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Digital signal processing - dsp' conversation and receive update notifications?