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General discussion

The space domain

In Part 1 of this series, I extended the concept of the Fourier transform from the time domain into the space domain. I pointed out that while the time domainis one-dimensional, the space domain is thee-dimensional. However, in order to keep the complexity of this module in check, we will assume that space is onlytwo-dimensional. This will serve us well later for such tasks as image processing.

(Three-dimensional Fourier transforms are beyond the scope of this module. I will write a module on using Fourier transforms inthree-dimensional space later if I have the time.)

A purely real space domain

Although the space domain can be (and often is) complex, many interesting problems, (such as photographic image processing) can be dealt with under the assumption that the space domain is purely real. We willmake that assumption in this module. This assumption will allow us to simplify our computations when performing the 2D Fourier transform to transform our datafrom the space domain into the wavenumber domain.

Preview

I will present and explain two complete Java programs in this module. The first program is a single class named ImgMod30 , which provides the capability to perform forward and inverse Fourier transforms onthree-dimensional surfaces. In addition, the class provides a method that can be used to reformat the wavenumber spectrum to make it more suitable for display.

The second program is named ImgMod31 . This is an executable program whose purpose is to exercise and to test the ImgMod30 class using several examples for which the results should already be known.

Sample programs

The class named ImgMod30

This class provides 2D Fourier transform capability that can be used for image processing and other purposes. The class provides three static methods:

  • xform2D : Performs a forward 2D Fourier transform on a purely real surface described by a 2D array of double values in the space domain to produce a complex spectrum in the wavenumberdomain. The method returns the real part, the imaginary part, and the amplitude spectrum, each in its own 2D array of double values.
  • inverseXform2D : Performs an inverse 2D Fourier transform from the complex wavenumber domain into the real space domainusing the real and imaginary parts of the wavenumber spectrum as input. Returns the surface in the space domain as a 2D array of double values. Assumes that the real and imaginary parts in the wavenumber domainare consistent with a purely real surface in the space domain, and does not return an imaginary surface for the space domain
  • shiftOrigin : The wavenumber spectrum produced by xform2D has its origin in the top-left corner with the Nyquist folding wave numbers near the center. This is not a very suitableformat for visual analysis. This method rearranges the data to place the origin at the center with the Nyquist folding wave numbers along the edges.

The class was tested using JDK 1.8 and Windows 7. The class uses the static import capability that was introduced in J2SE 5.0. Therefore, it should notcompile using earlier versions of the compiler.

Questions & Answers

Application of nanotechnology in medicine
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.
Damian
yes that's correct
Professor
I think
Professor
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
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
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
hi
Loga
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
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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